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diff --git a/44371-0.txt b/44371-0.txt new file mode 100644 index 0000000..96f831c --- /dev/null +++ b/44371-0.txt @@ -0,0 +1,5692 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 44371 *** + +Transcriber's Notes: + +Text between underscores represents _italics_, small capitals have been +transcribed as ALL CAPITALS. + +Curly brackets indicate {subscripts}; letters between square brackets +(such as [T] and [U]) represent the shape rahter than the letter itself. + +More Transcriber's Notes may be found at the end of this text. + + + + + + THE + ANATOMY OF BRIDGEWORK + + + + + THE + ANATOMY OF BRIDGEWORK + + BY + + WILLIAM HENRY THORPE + ASSOC. M. INST. C. E. + + WITH 103 ILLUSTRATIONS + + [Illustration] + + London + E. & F. N. SPON, LIMITED, 57 HAYMARKET + New York + SPON & CHAMBERLAIN, 123 LIBERTY STREET + + 1906 + + + + +PREFACE + + +In offering this little book to the reader interested in Bridgework, the +author desires to express his acknowledgments to the proprietors of +“Engineering,” in which journal the papers first appeared, for their +courtesy in facilitating the production in book form. + +It may possibly happen that the scanning of these pages will induce +others to observe and collect information extending our knowledge of +this subject--information which, while familiar to maintenance engineers +of experience, has not been so readily available as is desirable. + +No theory which fails to stand the test of practical working can +maintain its claims to regard; the study of the behaviour of old work +has, therefore, a high educational value, and tends to the occasional +correction of views which might otherwise be complacently retained. + + 60 WINSHAM STREET, + CLAPHAM COMMON, LONDON, S.W. + _October_, 1906. + + + + +CONTENTS + + + CHAPTER I. + + INTRODUCTION--GIRDER BEARINGS. + + PAGE + + Pressure distribution--Square and skew bearings--Fixed bearings-- + Knuckles--Rollers--Yield of supports 1 + + + CHAPTER II. + + MAIN GIRDERS. + + _Plate webs_: Improper loading of flanges--Twisting of girders-- + Remedial measures--Cracks in webs--Stiffening of webs--[T] + stiffeners 9 + + _Open webs_: Common faults--Top booms--Buckling of bottom booms-- + Counterbracing--Flat members 17 + + + CHAPTER III. + + BRIDGE FLOORS. + + Liability to defects--Impact--Ends of cross and longitudinal + girders--Awkward riveting--Fixed ends to cross girders--Plated + floor--Liberal depths desirable--Type connections--Effect of “skew” + on floor--Water-tightness--Drainage--Timber floors--Jack arches-- + Corrugated sheeting--Ballast--Rail joints--Effect of main girders + on floors 20 + + + CHAPTER IV. + + BRACING. + + Effect of bracing on girders--Influence of skew on bracing--Flat + bars--Overhead girders--Main girders stiffened from floor-- + Stiffening of light girders--Incomplete bracing--Tall piers--Sea + piers 34 + + + CHAPTER V. + + RIVETED CONNECTIONS. + + Latitude in practice--Laboratory experiments--Care in considering + practical instances--Main girder web rivets--Lattice girders + investigated--Rivets in small girders--Faulty bridge floor-- + Stresses in rivets--Cross girder connections--Tension in rivets-- + Defective rivets--Loose rivets--Table of actual rivet stresses-- + Bearing pressure--Permissible stresses--Proposed table--Immunity of + road bridges from loose rivets--Rivet spacing 45 + + + CHAPTER VI. + + HIGH STRESS. + + Elastic limit--Care in calculation--Impact--Examples of high stress + --Early examples of high stress in steel girders--Tabulated + examples--General remarks 61 + + + CHAPTER VII. + + DEFORMATIONS. + + Various kinds--Flexing of girder flanges--Examples--Settlement + deformations--Creeping--Temperature changes--Local distortions-- + Imperfect workmanship--Deformation of cast-iron arches 73 + + + CHAPTER VIII. + + DEFLECTIONS. + + Differences as between new work and old--Influence of booms and web + structure on deflection--Yield of rivets and stiffness of + connections--Working formulæ--Set--Effect of floor system-- + Deflection diagrams--Loads quickly applied--“Drop” loads--Flexible + girders--Measuring deflections--New method of observing deflections + --Effect of running load 85 + + + CHAPTER IX. + + DECAY AND PAINTING. + + Examples of rusting of wrought-iron girders--Girder over sea-water + --Rate of rusting--Steelwork--Precautions--Red-lead--Repainting-- + Scraping--Girders built into masonry--Cast iron--Effect of sea- + water on cast iron--Examples--Tabulated observations--Percentage of + submersion--Quality of metal 96 + + + CHAPTER X. + + EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES. + + Purpose--Methods of examination--Calculations--Stress in old work-- + Methods of reducing stress--Repair--Loose rivets--Replacing wasted + flange plates--Adding new to old sections--Principles governing + additions--Example--Strengthening lattice girder bracings--Bracing + between girders--Strengthening floors--Distributing girders 107 + + + CHAPTER XI. + + STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS. + + Principal methods in use--Method of calculation--Adjustments-- + Connections--Method of execution--Checks--Effect of skew on method + considered--Results of calculation for a typical case--Probable + error--Practical examples--Special case--Method of determining + flexure curves 122 + + + CHAPTER XII. + + CAST-IRON BRIDGES. + + Limitations of cast iron--Stress examples--Advantages and + disadvantages--Foundry stresses--Examples--Want of ductility of + cast iron--Repairs--Restricted possibilities 141 + + + CHAPTER XIII. + + TIMBER BRIDGES. + + Perishable nature--Causes of decay--Sag--Lateral bracing--Piles-- + Uncertainty respecting decay--Examples--Conditions and practice + favourable to durability--Bracing--Protection--Repair--Piles--Cost 149 + + + CHAPTER XIV. + + MASONRY BRIDGES. + + Definition--Cause of defects or failure--Spreading of abutments-- + Closing in--Example--Stop piers--Example of failure--Strength of + rubble arch--Equilibrium of arches--Effect of vibration on masonry + --Safety centring--Methods of repair--Pointing--Rough dressed + stonework 157 + + + CHAPTER XV. + + LIFE OF BRIDGES--RELATIVE MERITS. + + Previous history--Causes of limited life--Tabulated examples of + short-lived metallic bridges--Timber and masonry bridges-- + Durability--Maintenance charges--First cost--Comparative merits-- + Choice of material 165 + + + CHAPTER XVI. + + RECONSTRUCTION AND WIDENING OF BRIDGES. + + CONCLUSION. + + Measuring up--Railway under-bridges--Methods of reconstruction in + common use--Reconstruction of bridges of many openings--Timber + staging--Traffic arrangements--Sunday work--Railway over-bridges-- + Widenings--Junction of new and old work--Concluding remarks--Study + of old bridgework 172 + + INDEX 187 + + + + + THE + ANATOMY OF BRIDGEWORK. + + + + +CHAPTER I. + +INTRODUCTION. + + +No book has, so far as the author is aware, been written upon that +aspect of bridgework to be treated in the following pages. No excuse +need, therefore, be given for adding to the already large amount of +published matter dealing with bridges. Indeed, as it too often happens +that the designing of such constructions, and their after-maintenance, +are in this country entirely separated, it cannot but be useful to give +such results of the behaviour of bridges, whether new or old, as have +come under observation. + +In the early days of metallic bridges there was of necessity no +experience available to guide the engineer in his endeavour to avoid +objectionable features in design, and he was, as a result, compelled to +rely upon his own foresight and judgment in any attempt to anticipate +the effects of those influences to which his work might later be +subject. How heavily handicapped he must have been under these +conditions is evident from the mass of information since acquired by the +experimental study of the behaviour of metals under stress, and the +growth of the literature of bridgework during the last forty years. That +many mistakes were made is little occasion for surprise; rather is it a +cause for admiration that some very fine bridges, still in use, were +the product of that time. Much may be learned from the study of defects +and failures, even though they be of such a character that no +experienced designer would now furnish like examples. + +Modern instances may, none the less, be found, with faults repeated, +which should long since have disappeared from all bridgework, and are +only to be accounted for by the unnatural divorce of design and +maintenance already referred to. As the reader proceeds, it may appear +that details are occasionally touched upon of a character altogether too +crude and objectionable to need comment; but the consideration of these +cases is none the less interesting, and, so far as the author’s +observation goes, not altogether unnecessary. + +Most of the instances cited are of bridges, or parts of bridges, of +quite small dimensions; but it is these which most commonly give +trouble, both because the effects of impact are in such cases most +severely felt, and possibly because the smaller class of bridges is very +generally designed by men of less experience, than large and imposing +structures. + +The particulars given relate in all cases to bridges of wrought iron, +unless otherwise described. + +An endeavour has been made to secure some kind of order in dealing with +the subject, but it has been found difficult to avoid a somewhat +disjointed treatment, inseparable, perhaps, from the nature of the +matter. Finally, the reader may be assured that every case quoted has +come under the writer’s personal notice. + + +GIRDER BEARINGS. + +In girder-work generally, and more particularly in plate-girders, +considerable latitude obtains in the amount of bearing allowed. Clearly, +the surface over which the pressure is distributed should be +sufficiently ample to avoid overloading and possible crushing or +fracture of bedstones where these exist; but if no knuckles are +introduced, this is an extremely difficult matter to insure. A long +bearing may deliver the load at the extreme end of the surface on which +it rests, or, more probably, near the face. + +If the girder is made with truly level bearings, and the beds set level, +it will certainly, when under load, throw an extreme pressure upon that +part of the bearing surface immediately under the forward edge of the +bearing-plate. These considerations probably account for bedstones +frequently cracking, in addition to which possibility there is the +disadvantage that the designer does not know where the girder will rest, +and cannot truly define the span. The variation of flange-stress due to +this cause may, in a girder of ordinary proportions, having bearings +equal in length to the girder’s depth, be as much as 15 per cent. above +or below that intended. + +If great care be taken in setting beds, in the first instance, to dip +toward the centre of the span an amount depending upon the anticipated +girder deflection, it may be possible to insure that when under full +load the girder bearing shall rest equally upon its seat; but this is +evidently a difficult condition to obtain practically, is good only for +one degree of loading, and may at any time be nullified by a disturbance +of the supports, as, for instance, the very common occurrence of a +slight leaning forward of abutment walls. + +Double or treble thicknesses of hair-felt are sometimes placed beneath +girder bearings, with the object of securing a better distribution of +pressure, no doubt with advantage; but this practice, though it may be +quite satisfactory as applied to girders carrying an unchangeable load, +hardly meets the case for loads which are variable. Notwithstanding the +faulty nature of the plain bearing ordinarily used for girders of +moderate span, its extreme simplicity commends it to most engineers. It +must be admitted that no serious inconvenience need be anticipated in +the majority of cases, particularly if the bearings are limited in +length, do not approach nearer than 3 inches to the face of bedstones, +and are furnished with hair-felt or similar packing. + +[Illustration: FIG. 1.] + +Whether with long or short bearings, the forward edge should be at right +angles to the girder’s length. In skew bridges it is sometimes seen that +this edge follows the angle of skew. The effect on the girder is to +twist it, as will be clear from a little consideration. In evidence of +this the case may be quoted of a lattice girder of 95 feet effective +span and 7 feet deep, which, resting on a skew abutment right up to the +masonry face at a rather bad angle (about 15 degrees), was, after twenty +years, found canted over at the top to the extent of 4 inches, with the +further result of springing a joint in the top flange at about the +middle of the girder, causing some rivets to loosen. The bedstone was +also very badly broken at the face, and had to be replaced in the course +of repairs (Fig. 1). This girder had, in addition to the canting from +the upright position at its end, and the distortion of the top flange, a +curvature in the same direction, though less in amount, at the +bottom--an effect very common in the main girders of skew bridges, and +possibly accounted for in part by a tendency of the girder end to creep +along the abutment away from the point at which it bears hardest, under +frequent applications and removals of the live load, and accompanying +deflections. + +This tendency to travel may be aggravated in bridges carrying a +ballasted road, in which there may be a considerable thickness of +ballast near the bearings, by the compacting and spreading of this +material taking effect upon the girder end, tending to push it outwards, +being tied only by a few light cross-girders badly placed for useful +effect. The movement may be prevented in new work for moderate angles of +skew by carrying the end cross-girders well back, and securing them in +some efficient manner; or by the introduction of a diagonal tie +following the skew face, and attached to cross and main girder flanges +(Fig. 2)--a method which may be applied to existing work also. + +[Illustration: FIG. 2.] + +For such a case as that cited it is imperative that ballast pressure at +the girder end should be altogether eliminated. + +The fixing of girder ends by bolts--a practice at one time usual--hardly +calls for remark, as it is now seldom resorted to unless for special +reasons; but it may be well to point out the weakening effect of holes +for any purpose in bedstones. Bed-plates commonly need no fixing; the +weight carried keeps them in position, or if, in the case of very light +girders upon separate plates, it is considered well to secure these from +shifting, it may best be done by letting the plate in bodily a small +amount, or by means of a very shallow feather sunk into a chase. + +[Illustration: FIG. 3.] + +As an improvement upon the plain bearing usually adopted, it is an easy +matter so to design girder-ends as to deliver the load by a narrow strip +of bearing-plate carried across the bottom flange, distributing the +pressure upon the stone, if there be one, by means of a simple +rectangular plate of sufficient stoutness (Fig. 3). An imperfect knuckle +will by this means result, with freedom to slide, and the girder span be +defined within narrow limits. A true knuckle is, of course, the best +means of securing imposition of the load always in the same place; but +this by itself is not sufficient where the girder is of a length to make +temperature and stress variations important, in which case rollers, or +freedom to slide, become necessary. Bridges exist in which +roller-bearings have been adopted without the knuckle, or its +equivalent, but this is wholly indefensible, as it is obvious that the +forward roller will in all probability take the whole load, and cannot +be expected to keep its shape and roll freely under this mal-treatment. +It is sometimes asserted that rollers are never effective after some +years’ use; that they become clogged with dirt, and refuse to perform +their office. + +There is no reason why rollers should not be boxed in to exclude dirt by +a casing easily removed, some attention being given to them, and any +possible accumulation of dirt removed each time the bridge is painted. + +To test the behaviour of rollers under somewhat unfavourable conditions +for their proper action--that of the bearings of main roof trusses of +crescent form, 190 feet span--the author, some thirty years since, took +occasion to make the necessary observations, and found evidence of a +moderate roller movement, though there was in this case no direct +horizontal member to communicate motion. With girders resting upon +columns, particularly if of cast iron, a roller and knuckle arrangement +is most desirable for any but very small spans, as, if not adopted, the +result will be a canting of the columns from side to side--a very small +amount, it is true, but sufficient to throw the load upon the extreme +edges of the base, though the knuckle alone will relieve the top of this +danger. The author at one time took the trouble to examine, so far as it +could be done superficially and without opening out the ground to make a +complete inspection possible, a number of bridges crossing streets, in +which girders rested upon and were secured to cast-iron columns standing +in the line of kerb; and he found cracks, either at the top or bottom, +in about one of every four columns. + +When girders passing over columns are not continuous, it may be +difficult to find room for a double roller and knuckle arrangement; but +this inconvenience may be overcome by carrying one girder-end wholly +across the column-top, and securing the next girder-end to it in a +manner which a little care and ingenuity will render satisfactory, one +free bearing then serving to carry the load from both girders. + +Though the wisdom of using rollers is apparent in spans exceeding some +moderate length, say 80 feet--as to which engineers do not seem quite +decided--and varying with the conditions, it need not be overlooked that +in some cases masonry will be sufficiently accommodating to render them +unnecessary; piers, if sufficiently tall and slender, will yield a small +amount without injury, and though shorter, if resting upon a bottom not +absolutely rigid, will rock and give the necessary relief; but it is +obvious, if the resistance to movement is sufficiently great, and the +girder cannot slide or roll on its bearings, bedstones will probably +loosen, as, indeed, frequently happens. + + + + +CHAPTER II. + +MAIN GIRDERS; PLATE-WEBS. + + +It is seldom that girders of this description--or, indeed, of any +other--show signs of failure from mere defect of strength in the +principal parts, even though somewhat highly stressed; and instances +tending to support this statement will be given in a later chapter. For +the present, it is proposed to indicate peculiarities of behaviour only, +generally, but not always, harmless. + +Though now less often done, it was at one time common practice to load +plate-girders on the bottom flange by simply resting floor timbers, +rails, troughs, or cross-girders upon them. In outside girders one +result of this is to cause the top flange to take a curve in plan, +convex towards the road, every time the live load comes upon the floor +of the bridge, upon the passing of which the flange resumes its figure, +though still affected by that part of the load which is constant. + +A bridge of 47 feet span, carrying two lines of way, having one centre +and two outside girders, with a floor consisting of old Barlow rails, +resting upon the bottom flanges, showed the peculiarity named in a +marked degree. + +The outside girders, under dead load only, were, as to the top flanges +(see Figs. 4 and 5), 1-1/4 inch and 1-1/16 inch respectively out of +straight in their length, but upon the passing of a goods engine and +train curved an additional 1-1/8 inch, or 2-3/8 inches in all, for one +outside girder, and 2-3/16 inches for the other. + +The centre girder, having a broader and heavier top flange, curved 5/8 +inch towards whichever road might be loaded. The effect of such +horizontal flexure is clearly to induce stresses of tension and +compression in the flanges, which, being (for the top flange) compounded +with the normal compressive stress due to load carried, results in a +considerable want of uniformity across the section. + +[Illustration: FIG. 4.] + +In the case under notice, the writer estimates the stresses for an outer +girder top flange at 4·5 tons per square inch compression for simple +loading, and 5·5 tons per square inch of tension and compression, on the +inner and outer edges, due to flexure, resulting when compounded in a +stress of 1 ton per square inch tension on the inside, and 10 tons per +square inch compression on the outside edge. In this rather extreme case +the stress on the inner edge, or that nearest the load, is reversed in +character. + +The effect described appears to be not wholly due to the twisting +moment. It is apparent that whatever curvature may be induced by +twisting alone must be aggravated in the compression flange by its being +put out of line. + +The writer does not attempt here to apportion the two effects in any +other way than to say that the greater part of the flexure appears to be +due to the secondary cause. Consistent with this view of the matter is +the fact that the inclination of the girder towards the rails greatly +exceeded the calculated slope of the Barlow rail-ends when under load, +being about five times as great. The inference is that the floor rails +bore hard at their extreme ends, at which point of bearing the +calculated twisting moment accounts for less than one-half of the +flexure observed in the flanges. + +[Illustration: FIG. 5.] + +The girders upon removal in the course of reconstruction again took the +straight form, showing that the very frequent development of the +stresses named had not sensibly injured the metal, though the bridge +carried as many as three hundred trains daily in each direction, and had +done so for very many years. + +The deformation of the top flange only has been noticed, yet the same +tendency exists in the bottom, though the actual amount is much less, +both because the lower flanges are in tension, and are also in great +degree confined by the frictional contact of the cross bearers, even +where no proper ties are used. In the case dealt with the bottom flanges +of the outer girders curved 1/8 inch outwards only. + +With the broad flanges commonly adopted in English practice, twisting of +the girders, under conditions similar to the above, will not generally +be a serious matter; but with narrow flanges possessing little lateral +stiffness it might be a source of danger. + +[Illustration: FIG. 6. FIG. 7.] + +The twisting may be limited in amount by introducing a cross-frame +between the girders, from which they are stiffened; by strutting the +girders immediately from the floor itself, in which case they cannot +cant to a greater extent than that which corresponds to the floor +deflection; or by designing the top flange to be unsymmetrical with +reference to the web, as in Figs. 6 and 7, with the object of insuring +that under the joint effect of vertical loading and twisting, the stress +in the flange shall at maximum loads be uniform across the section, and +allow it to remain straight. This may be secured by making the +eccentricity of the flange section equal to that of the loading. For +instance, if the load be applied 3 inches away from the web centre, the +flange should have its centre of gravity 3 inches on the other side of +the centre line. It can be shown that this is true throughout the length +of the girder, and irrespective of the depth. An instance in which +flange eccentricity being in excess, curvature outwards resulted, will +be found in a later chapter on deformations, etc. It will not generally +be necessary to make the bottom flange eccentric, as it is commonly tied +in some way; but if done, the eccentricity should be on the same side as +for the top. The flanges remaining straight under these conditions are +not subject to the complications of stress referred to in the case first +quoted. The author has adopted both the last named details in bridges +where he has been obliged to accept unfair loading of the kind +discussed. + +It should be remarked that by the two first methods, if the stiffening +frames are wide apart and attached direct to the web, there is a +liability for this to tear, under distress, rather than keep the girder +in line. + +There is one other possible consequence of throwing load upon the +flanges of a girder of a much more alarming nature. In girders not very +well stiffened, it may happen that the frequent application of load in +this manner finally so injures the web-plate, just above the top edge of +the bottom angle-bars, as to cause it to rip in a horizontal direction. +More likely is this to happen with a centre girder taking load first on +one side, then on the other, and again on both together. Cases may be +cited in which cracks right through the webs 3 feet or more in length +have resulted from this cause. It is very probable, however, that in +some of these cases the matter was aggravated by the use of a poor iron +in the webs, as at one time engineers, from mistaken notions of the +extreme tenuity permissible in webs near the centre of a girder, would, +if they could not be made thin enough, even encourage the use of an +indifferent metal as being quite good enough for that part of the work. + +An instance of web-fracture from somewhat similar causes may be here +given. + +In a bridge of 31 feet 6 inches effective span, and consisting of twin +girders carrying rails between, as shown in Figs. 8 and 9, the load +resting upon the inner ledges, formed by the bottom flange, induced +such a bending and tearing action along the web just above the +angle-bars, as to cause a rip in one of the girders, well open for some +distance, and which could be traced for 14 feet as a continuous crack. + +[Illustration: FIG. 8.] + +[Illustration: FIG. 9.] + +It will be noticed in the figure that the [T] stiffeners occur only at +the outer face of the web, and that the inner vertical strips stop short +at the top edge of the angles, the result being that under load the +flange would tend to twist around some point, say A, at each stiffener, +inducing a serious stress in the thin web at that place, while away from +these stiffeners the web would be more free to yield without tearing. +The fact that at a number of the stiffeners incipient cracks were +observed, some only a few inches long, suggests this view of the matter. + +A case of web-failure from other influences coming under notice showed +breaks at the upper part of the web extending downwards. + +In this bridge, of 32 feet span, which had been in existence thirty-two +years, the webs--originally 1/4 inch thick--were, largely because of +cinder ballast in contact with them, so badly wasted as to be generally +little thicker than a crown-piece, and in places were eaten through; in +addition to which, the road being on a sharp curve, the rail-balks had +been strutted from the webs to keep them in position, the effect of +which would be to exert a hammering thrust upon the face of the web at +the abutting ends, and assist in starting cracks in webs already much +corroded. A feature of this case, tending to show that the breaks +resulted as the joint effect of waste and ill-usage by the strut +members, rather than by excessive stress in the web as reduced, is to be +found in the fact that the girders when removed were observed to be in +remarkably good shape--i.e. the camber, marked on the original drawings +to be 1-1/2 inch, still showed as a perfectly even curve of that rise, +which would hardly have been the case if the lower flange had been let +down by web-rupture, the result of excessive web-stresses. + +Occasionally webs will crack through the solid unwasted plate, in a line +nearly vertical; not where shear stress is greatest, but generally at +some other place, and from no apparent cause, either of stress or +ill-usage. The writer has observed this only in the case of small +girders not exceeding 2 feet in depth; and, for want of any better +reason, attributes these cracks to poor material, coupled with some +latent defect. In a bridge having some thirty cross-girders, each 26 +feet long, about every other one had a web cracked in this manner after +many years’ use. + +Web-cracks of the kind first indicated, are perhaps, the most probable +source of danger in plate-girders, of any which are likely to occur. The +fault is insidious, difficult to detect when first developed, and +perhaps not seen at all till the bridge, condemned for some other +reason, has the girders freely exposed and brought into broad light. The +manner in which old girders are sometimes partly concealed by +timberwork, or covered by ballast, makes the detection of these defects +an uncertain matter, unless sufficient trouble is occasionally taken to +render inspection complete. + +The manner in which girders with wasted and fractured webs will still +hang together under heavy loading seems to warrant the deduction that, +in designing new work, it can hardly be necessary to provide such a +considerable amount of web-stiffening as is sometimes seen; experience +showing that defects of the web-structure do not commonly occur in the +stiffening so frequently as in the plate, and then in the form of +cracks. + +A case of web-buckling lies, so far, without the author’s experience. +There is no need to introduce, for web-stresses alone, more stiffening +than that which corresponds to making the stiffeners do duty as vertical +struts in an openwork girder; in which case it is sufficient to insure +that the stiffeners occurring in a length equal to the girder’s depth +shall, as struts, be strong enough in the aggregate to take the whole +shear force at the section considered, in no case exceeding this amount +on one stiffener. For thin webs in which the free breadth is greater +than one hundred and twenty times the thickness, the diagonal +compressive stress may be completely ignored, and the thickness +determined with reference to the diagonal tension stress only. + +There is one fault which frequently shows itself in stiffeners though +not the result of web-stresses, and when performing an additional +function--viz., the breaking of [T] stiffener knees at the weld, where +brought down on to the tops of cross-girders, due to the deflection of +the floor, as shown in Fig. 10. When such knees are used, the angle may +properly be filled in with a gusset-plate to relieve the weld of strain +and prevent fracture. + +[Illustration: FIG. 10.] + +There is some little temptation in practice to make use of the solid web +as a convenient stop for ballast, or road material. Special means, +perhaps at the cost of some little trouble, should be adopted, where +necessary, to avoid this. + + +MAIN GIRDERS; OPEN WEBS. + +With these, as with plate-girders, deficiency of strength--i.e. of +section strength--is seldom so marked as to be a reasonable cause of +anxiety. In particular instances faults in design may result in stresses +of an abnormal amount, though rarely to an extent occasioning any ill +effects. The practice of loading the bottom flanges at a distance from +the centre, the bad effects of which have already been dealt with as +applied to plate-girders, is not commonly resorted to in girders having +open webs, nor are these so liable to be heaped with ballast in +immediate proximity to essential members of the structure. + +Some defects are, however, occasionally seen which may be remarked. Top +booms of an inverted [U] section are sometimes made with side webs too +thin, and having the lower edges stiffened insufficiently, or not at +all. Where this is the case, the plates may be seen to have buckled out +of truth, showing that they are unable, as thin plates, to sustain the +compressive stress to which the rest of the boom is liable. The practice +of putting the greater part of the boom section in an outer flange, +characteristic of this defect, has the further disadvantage of throwing +the centre of gravity of the section so near its outer edge as to make +impracticable the best arrangement of rivets for connection of the web +members. Further, since all the variation in boom section is thrown into +the flange-plates, the centre of gravity of the section has no constant +position along the boom--an additional inconvenience where correct +design is aimed at. + +These considerations indicate the propriety of arranging the bulk, or +all, of the section at the sides, thus reducing or getting rid of the +objections named. + +Where the bottom boom consists of side plates, only one point demands +attention. It is found that, though nominally in tension, the end bays +are liable occasionally to buckle, as though under compressive stress, +and need stiffening, not excepting girders which at one end are mounted +on rollers. This might seem to indicate that the rollers are of no use; +but it is conceivable the resistance arises from other causes, such as +wind forces, or as in the case of a bridge carrying a railway, in which +the rigidity of the permanent-way may be such that the bridge-structure, +in extending towards the roller end, cannot move it sufficiently, +causing a reversal of stress on the lighter portions of the bottom boom +at the knuckle end; or by the exposed girder booms becoming very +sensibly hotter than the bridge floor, and by expanding at a greater +rate, cause this effect, from which rollers cannot protect them. + +In counterbracing consisting of flat bars it is desirable either to +secure these where they cross other members, or stiffen them in some +manner to avoid the disagreeable chattering which will otherwise +commonly be found to occur on the passage of the live load. + +Occasionally diagonal ties are made up of two flat bars placed face to +face, to escape the use of one very thick member. Where this is done, +the two thicknesses, if not riveted together along the edges, will be +liable to open, as the result of rusting between the bars in contact, +when the evil will be aggravated by the greater freedom with which +moisture will enter the space. + +Other matters relating to open-web girders will be more conveniently +dealt with under their separate headings, particularly a further +consideration of the relationship subsisting between the booms and floor +structure. + + + + +CHAPTER III. + +BRIDGE FLOORS. + + +The floors of bridges commonly give more trouble in maintenance, and +their defects are more frequently the cause which renders reconstruction +necessary, apart from reasons not concerning strength, than any other +part of such structures. When it is considered that this portion of a +bridge is first affected by impact of the load which comes upon it, and +is usually light in comparison with the main girders further removed +from the load, and to which the latter is transferred through the more +or less elastic floor, the fact will be readily appreciated by those not +already familiar with it. + +The end attachments of cross and longitudinal girders are very liable to +suffer by loosening of rivets, or, more rarely, by breaking of the +angle-irons which commonly make such a connection. A not unusual defect +of old work, which may also sometimes be seen in work quite new, where +the cross-girder depth has from any cause been restricted, is the +extremely cramped position of the rivets securing the ends. There is +small chance of these ever being properly tight, if the act of riveting +is rendered difficult by bad design. This is the more objectionable if +it happens that cross-girder ends abut against opposite sides of the web +of an intermediate main girder, and are secured by the same rivets +passing through. At the best such rivets will not be well placed to +insure good workmanship, and the severe treatment to which they become +subject, as the cross-girders take their load and deflect under it, +will be very apt to loosen them. The author has seen a case of this kind +(see Figs. 11 and 12)--rather extreme, it is true--in which nearly the +whole of the cross-girder end rivets were loose, some nearly worn +through, thus allowing the cross-girders to be carried, not by their +attachments, but by resting upon the main-girder flanges, which in turn, +by repeated twisting, tore the web for a length of 4 feet; there was +also pronounced side flexure of the top booms. The movements generally +on this bridge (of 42-feet span), whether of main or cross-girders, were +very considerable and disturbing. It was removed after about +twenty-three years’ use. + +[Illustration: FIG. 11.] + +[Illustration: FIG. 12.] + +There is no necessity, as a rule, for the ends of cross-girders attached +to the same main girder at opposite sides to be placed in line. The +author prefers to arrange them to miss, by which device each connection +is entirely separate, the riveting can be more efficiently executed, +erection is simplified, and the rivets will be more likely to keep +tight. Other special cases of cross-girder ends will be dealt with under +the head “Riveted Connections.” + +It is sometimes contended that cross-girders attached at their ends by a +riveted connection should be designed as for fixed ends, in which case +they are usually made of the same flange section throughout, with a view +to satisfy the supposed requirements. But a girder to be rightly +considered as having fixed ends must be secured to something itself +unyielding. With an outer main girder of ordinary construction, and no +overhead bracing, this is so far from being the case as to leave little +occasion for taking the precaution named. As the cross-girders deflect, +the main girders will commonly yield slightly, inclining bodily towards +the cross-girders, if these are attached to the lower part of the main +girders. The force requisite to cant the main girders in this manner is +usually less than that which corresponds to fixing the cross-girder +ends, and is, generally, slight. It is, of course, necessary that this +measure of resistance at the connection should be borne in mind for the +sake of the joint itself, quite apart from any question of fixing. + +Possibly, in quite exceptional cases, where very stiff main girders are +braced in such a manner as to prevent canting, it may be proper to +consider the cross-girder ends as fixed, or for those near the bearings +of heavy main girders; but the author has not met with any example where +cross-girders, apart from attachments, appear to have suffered from +neglect of this consideration. + +With cross-girders placed on either side of a main girder, and in line, +it may also, for new work, be desirable to regard the ends as fixed, and +to detail them with this in view. It does not, however, appear wise to +carry this assumption to its logical issue, and reduce the flange +section to any appreciable extent on this account. The fixity of the +ends will, in any such case, be imperfect; and when one side only of an +intermediate main girder is loaded, it can have but a moderate effect in +reducing flange stress at the middle of the loaded floor beam. + +[Illustration: FIG. 13. FIG. 14. FIG. 15.] + +Similar reasons affect the design of longitudinal girder attachments to +cross-girders, which, if intended to support rails, cannot of necessity +be schemed to come other than in line. Where the floor is plated as one +plane surface, there will not usually be any trouble resulting if no +special precautions are used, as the plate itself will insure that the +longitudinals act, in a measure, as continuous beams, relieving the +joints of abnormal stress. If the plating is, however, designed in a +manner which does not present this advantage, or if the floor be of +timber, it is better to decide whether the connections shall be +considered as fixed, and made so; or avowedly flexible, and detailed in +such a manner as to possess a capacity for yielding slightly without +injury. Those connections are most likely to suffer which are neither of +the one character nor the other, offering resistance without the ability +to maintain it. Figs. 13, 14, and 15 give representations of three +“spring joint” methods of insuring yield in a greater or less degree. +For small longitudinals it is, perhaps, sufficient to use end angles +with very broad flanges against the cross-girder web; these to be +riveted in the manner indicated in Fig. 15. + +Liberal depth to floor beams is distinctly advantageous where it can be +secured, rendering it easier to design the ends in a suitable manner, by +giving room near mid-depth of the attachment to get in the necessary +number of rivets; or where the ends are rigidly attached direct to +vertical members of an open-work truss, the greater depth is effective +in reducing the inclination of the end from the vertical, with a +correspondingly reduced cant of the main girders and flexure of the +vertical member, with smaller consequent secondary stresses. In any case +deep girders will contribute to stiffness of the floor itself, +favourable in railway bridges to the maintenance of permanent-way in +good order. + +[Illustration: FIGS. 16, 17, 18.] + +A point in connection with skew-bridge floors occasionally overlooked is +the combined effect of the skew, and main girder camber, in throwing the +floor structure out of truth, if no regard has been paid to this. The +result is bad cross-girder or other connections; or, in the case of +bearers running over the tops of main girders, a necessity for special +packings to bring all fair (Fig. 17). The author has in such cases, +where cross-girders are used, set the main girder beds at suitable +levels, in order that the cross-bearers may all be horizontal (see Figs. +16 and 18). This may not always be permissible; but, however the +difficulty may be met, it should be dealt with as part of the design. +For small angles of skew only may it be neglected. + +Rivets attaching cross-girder angles to the web will occasionally +loosen, probably due in most cases to bad work, together with some +circumstance of aggravation, as in the case of a bridge floor consisting +of girders spaced 3 feet 6 inches apart, with short timber bearers +between, carrying rails. In many girders the top row of rivets, of +ordinary pitch and size, had loosened, allowing the web, about 1/4 inch +thick, a movement of 1/8 inch vertically. The rails being very close +down upon the cross-girder tops, though not intended to touch, had at +some time probably done so, and by “hammering” produced the result +described. + +Plated floors are often found which are objectionable on account of +their inability to hold water, arising sometimes from bad work, as often +from wide spacing of rivets. With rivets arranged to be easily got at, +and pitched not more than 3 inches apart, a tight floor may be expected; +but it is still necessary to drain the floor by a sufficient number of +holes, provided with nozzles projecting below the underside of the +plate, and sufficiently long to deliver direct into gutters, where these +are necessary. Drain-holes should not be less frequent than one to every +50 square feet of floor, if flat, and may advantageously be more so. +Gutters should slope well, and care be taken to insure practicable +joints and good methods of attachment--a matter too often left to take +care of itself, with considerable after-annoyance as a result. + +The use of asphalt, or asphalt concrete, to render a plated floor +water-tight is hardly to be relied upon for railway bridges, though no +doubt effective for those carrying roads. It is extremely difficult to +insure that it shall stand the jarring and disturbance to which it may +be subject, and under which it will commonly break up, and make matters +worse by holding moisture, and delaying the natural drying of the floor. +In bulk, as in troughs, it may be useful, but in thin coverings on +plates it cannot be depended upon. + +Floors having plated tops are sometimes finished over abutments or piers +in a manner which is not satisfactory, either as regards the carrying of +loads or accessibility for painting. If the plates are carried on to a +dwarf wall with the intention that the free margin of the plate shall +rest upon it, there will be a difficulty in securing this in an +efficient manner. Commonly such a wall is built up after the girder work +is in place, making it difficult to insure that the wall really supports +the plate, the result being that this may have to carry itself as best +it can. In any case, severe corrosion will occur on the underside, and +the plate rust through much before the rest of the floor; the masonry +also will usually be disturbed. + +It appears preferable to form the end of the floor with a vertical +skirting-plate having an angle or angles along the lower edge. This may +come down to a dwarf wall, but preferably not to touch it, the skirting +being designed to act as a carrying girder. A convenient arrangement is +shown in Fig. 19, which may be used either for a square or skew bridge. +It will be seen that the plate-girders have no end-plates, the skirting +referred to being carried continuously along the floor edge, and +attached to each girder-web, the whole of the more important parts being +open to the painter. + +[Illustration: FIG. 19.] + +Trough floors consisting of one or other of the forms of pressed or +rolled section present the objection that it is almost impracticable to +arrange an efficient connection at the ends, if they abut against main +girders, and but little connection is, as a rule, attempted, and +sometimes none. The result is that the load from these troughs is +delivered in an objectionable manner, and the ends being open or +imperfectly closed, water and dirt escape on to the flange, or other +ledge, which supports them. A description of pressed floor which +promises to overcome this objection, and provide a ready means of +attachment to the webs of plate-girders, or of booms having vertical +plate-webs, has within the last few years been introduced. This has the +ends shaped in such a manner as to close them and provide a flat surface +of sufficient area for connection by rivets. Each hollow is separately +drained by holes with nozzles. Whether this type of trough will develop +faults of its own, due to over-straining of the metal in the act of +pressing, remains to be seen; but as it appears possible to produce the +desired form without any material thinning or thickening of the metal, +the contention that no severe usage accompanies the process appears to +be reasonable. + +That form of troughing in which the top and bottom portions are +separately formed, and connected by a horizontal seam of rivets at +mid-depth, is found in use upon railway bridges to be very liable to +loosening of those rivets near the ends; less surprising, perhaps, +because the sloping sides are usually thin. + +It is a distinctly difficult matter to join two or more lengths of any +trough flooring having sloping sides, in a workmanlike manner; the fit +of covers is apt to be imperfect, and some rivets, being difficult of +access, are likely to be but indifferently tight, so that if the joint +occurs where it will be more than lightly stressed, trouble will +probably follow. A bad place for such joints is immediately over girders +supporting the troughs, as there the stress will be most severe, any +leakage come directly upon the girder, and remedial measures be more +difficult to carry out. + +Timber floors of the best timber, close jointed, are more durable than +might be supposed. The disadvantage is a difficulty in ascertaining the +precise condition of the timber after many years’ use. The author has +seen timbers, 9 inches by 9 inches, forming in one length a close floor, +carried by three girders, and supporting two lines of way, which, when +taken out, could as to a considerable part be kicked to pieces with the +foot; whilst in another case, with the same arrangement of girders and +close-timbered floor, the wood, after being in place for thirty-two +years, was, when taken out, found to be perfectly sound, with the +exception of a very few bad places of no great extent. In this instance, +however, it is known that the floor--pitch-pine--was put in by a +contractor who prided himself upon the quality of the timber that he +used; the floor being also covered with tar concrete, which had in this +instance so well performed its office as to keep the timber quite dry on +the top. + +Jack arches between girders make an excellent floor for road bridges, +though heavy; and for small bridges may be used to carry rails, if the +girders are designed to be stiff under load. The apprehension that +brickwork or concrete will separate from the girder-work, or become +broken up under even moderate vibration, does not seem to be well +founded, if the deflection is small and the brickwork or concrete good. + +The use of corrugated sheeting as a means of rendering the underside of +a bridge drop dry cannot be too strongly deprecated. If it must be +adopted, the arrangement should be such as to permit ready removal for +inspection and painting. It is evident that by boxing up the floor +structure, rust is favoured, and serious defects may be developed, not +to be discovered till the sheeting is removed, or something happens. + +[Illustration: FIG. 20.] + +A case may be instanced in which it was found, on taking down sheeting +of this description, that the floor girders, previously hidden, were +badly wasted in the webs. One of these girders had cracked, as shown in +Fig. 20, and others were in a condition only less bad. + +In any floor carrying ballast or macadam, if means are not adopted to +keep the road material from the structure of the floor, or from the main +girders, corrosion may be serious in its effects. Cinder ballast is, +perhaps, the worst in this respect, in its action upon steel or +ironwork, being distinctly more damaging than any other kind commonly +used. + +Rail-joints upon bridge floors are to be avoided where practicable by +the use of rails as long as can be obtained; if the bridge is small +enough, crossing it in one length. At each joint there is likely to be +hammering and working extremely detrimental to floor members and +connections; indeed, it may happen that loose rivets will be found in +the neighbourhood of such joints, and nowhere else on the bridge. Where +rail-joints cannot be avoided, their position should, if there be any +choice, be judiciously selected, and the plate-layers taught to close +the joints and jam the fish-bolts. + +[Illustration: FIG. 21.] + +As rail-joints upon a bridge may injuriously affect the floor, so also +will a weak floor be very trying to the rails. A remarkable instance of +this has come under the writer’s notice, where a bridge (Fig. 21) of +three 33-feet spans, having outer and centre main girders, with +cross-girders spaced 3 feet apart, resting upon the girder flanges, but +not attached, and carrying two roads, had the permanent-way in a very +bad state. The rails proper, with supplementary angle-plates, rested +direct upon the cross-girders, which were decidedly light, and the whole +floor had much “life” in it, the ill-effect of which was shown in +thirteen breaks in the angle-plates, in each case near their ends, +generally at holes. + +It appears probable that severe stresses may be thrown upon the parts of +a floor, whether placed at the level of the bottom booms or of the top, +by changes of length in the booms due to stress. The author has, +unfortunately, no direct evidence to offer in reference to this, tending +either for or against the contention. If an unplated floor of cross and +longitudinal girders of usual arrangement be at the bottom boom of a +large bridge, as the boom lengthens with the imposition of load upon the +bridge, all the cross-girders from the centre towards the abutments will +be curved horizontally, the middle portion being restrained by the +longitudinals from moving bodily with the ends. Each cross-girder except +that at the centre, if there be one, will thus present a figure in plan, +concave towards the abutment to which it is nearest. This will be +accompanied by stressing of the connections, and a transfer to the +longitudinals of as much of the tensile stress properly belonging to the +booms as the stiffness of the cross-girders may communicate. + +This in itself will hardly be considerable, and will be the less on +account of a slight yielding which may be expected at the end +connections of each longitudinal; but the effect upon the cross-girders +by horizontal bending will be much marked. If the case be supposed of a +200-feet span in steel at ordinary loads and stresses, carrying one line +of way, with cross-girders 20 feet apart, and having no floor-plates, it +may be ascertained, neglecting for the moment any slight yielding of the +longitudinal girder connections, that upon the bridge taking its full +live load there will be the following approximate results: Movement at +each end of the end cross-girders of 3/10 inch, equivalent to a force of +7-1/2 tons, tending to bend them horizontally, and a mean stress on the +outer edges of the girders, 12 inches wide, of 8 tons per square inch +due to flexure, which, compounded with the ordinary flange stresses, +will seem to give rather alarming results. There will also be a +longitudinal stress in the rail-girders, at centre part of bridge, of +3/4 ton per square inch. Normal elongation of the longitudinal girder +bottom flanges, and compression of the top, modifies the figures +unfavourably as to the cross-girder top flange. Yielding of the +connections named before has been neglected in arriving at these +stresses. If they are sufficiently accommodating to give freely, to a +mean extent, as between the top and bottom of each joint, of 1/29 inch, +these results will disappear. It is evident, however, that we cannot +rely upon good work yielding without the existence of considerable +forces to cause it. In the issue it is justifiable to apprehend that the +flexing and stressing of the cross-girders will be considerable. + +The most favourable case has been taken; if now it is assumed that the +floor has continuous plating, the results would seem to be much more +astonishing. It will appear on this supposition that the boom stresses, +instead of being taken wholly by the booms, are about equally divided +between these and the floor structure, each cross-girder connection +communicating its share of boom stress to the floor, which for the end +cross-girders will approach 40 tons at each connection--considerably +more than the vertical reaction under normal loads. + +Palpably, these conclusions must be greatly modified by the yield of +longitudinal girder ends, and slip of the floor rivets in transverse +seams. If these rivets be 3-1/2 inch pitch and 3/4 inch in diameter, the +stress at each, as estimated, would be sufficient to induce shear of +about 6 tons per square inch--more than enough to cause “slip.” After +making this allowance, it is still evident there must be very serious +forces at work about the ends of cross-girders under the conditions +supposed, probably not less than one half the amounts named, as with +this reduction the floor rivets should not yield, given reasonably good +work. It is to be observed that the effect of live load only has been +introduced, on the presumption that the longitudinals and floor-plating +have not been riveted up till the main girders have been allowed to +carry the major part of the dead load; but even this cannot always be +conceded. The deduction appears to be that the floor and cross-girder +connections should be studied with special reference to these possible +effects, either with the object of rendering the communication of these +forces harmless, or making the floor so that it shall take little or no +stress from the main booms, by arranging joints across the floor +specially designed to yield, the ends of longitudinals being schemed +with the same object. Where there is no plating, the case is, perhaps, +sufficiently provided for by making the cross-girders narrow, and the +longitudinal girder connections flexible, or by putting these girders +upon the top of the cross-girders, when stretching of the bottom flanges +of the rail-bearers under load may be expected, within a little, to keep +pace with the lengthening of the main booms. + +It would appear that light pressed troughs running across the +longitudinals would, by yielding in every section, also furnish relief, +as compared with the rigidity of flat plates. + +By placing the floor at a level corresponding to the neutral axis of the +main girders, the communication of stress to the floor may be avoided; +but it seldom happens that there is so free a choice as to floor height +relative to the girders. This solution is, therefore, of limited +application. + +It is obvious that somewhat similar effects must obtain to those +considered in detail, when the floor structure lies at the level of top +booms, but with forces of compression from the booms to deal with, +instead of tension. + + + + +CHAPTER IV. + +BRACING. + + +Bracing, whether to strengthen a structure against wind, to insure the +relative positions of its parts, or for any other purpose, cannot be +arranged with too great care and regard to its possible effects. Forces +may be induced which the connections will not stand, with loose rivets +as a consequence, and inefficiency of the bracing itself; or, the +connections holding good, stresses in the main structure may, perhaps, +be injuriously altered. + +To take a not uncommon case, let us suppose a bridge consisting of four +main girders placed immediately under rails of ordinary gauge, and +braced in vertical planes only, right across from one outer girder to +the other. If the roads were loaded always at the same time, nothing +objectionable would result; but, as a fact, this will be the exception. +When one pair of girders only takes live load, and deflects, the bracing +under the six-foot will endeavour to communicate some part of this load +to the other pair of girders. If the bracing is so designed that some +correctly calculated portion of the load can be transferred in this +manner, without over-stressing the bars and riveted connections, there +will be no harmful consequences; but if not, the bracings will most +probably work at the ends; this, indeed, is what frequently happens. +There is one other effect which will ensue, if the bracing is wholly +efficient; a certain twisting movement of the bridge will occur, which +increases the live load upon the outer girder on the loaded side of the +bridge to the extent of 10 per cent., with a corresponding lifting force +at the outer girder on the unloaded side. These amounts are not serious, +but wholly dispose of any advantage it is conceived will be gained by +causing the otherwise idle girders to act through the medium of the +bracing. In road bridges of similar arrangement, over which heavy loads +may pass on any part of the surface, it is clear that the use of bracing +between girders should not be taken as justifying the assumption that +the load is distributed over many girders, and correspondingly light +sections adopted, unless the effect of twisting on the whole bridge is +also considered, and justifies this view; for, as already stated in the +case of the railway bridge, the net result may be to increase the girder +stresses instead of reducing them. Generally, it may be deduced that the +better plan for railway bridges is to brace the girders in pairs, +leaving, in the case supposed, no bracing between the two middle +girders, though there will be no objection to connecting these by simple +transverse members of no great stiffness, to assist in checking lateral +vibration. For road bridges of more than five longitudinal girders, +equally spaced, it may be advantageous to brace right across, the +twisting effect with this, or a greater, number of girders not, as a +rule, leading to any increase of load on any girder. Figs. 22 to 25 give +the distribution of live load, placed as shown, for 3, 4, 5, and 6 +girders. + +It is to be observed that these statements do not apply to cases where +there may be also a complete system of horizontal bracing, the effect of +which, in conjunction with cross diagonals, may be greatly different, +with considerable forces set up in the bracing, and a modification of +girder stresses. + +These effects may be so considerable as to call for special attention in +design where such an arrangement is adopted. + +[Illustration: FIG. 22.] + +[Illustration: FIG. 24.] + +[Illustration: FIG. 23.] + +[Illustration: FIG. 25.] + +Somewhat similar straining to that first indicated may occur in bracings +placed between the girders of a bridge much on the skew. If this is, on +plan, at right angles to the girders, as is commonly and properly the +case, the ends will evidently be attached to the girders at points on +their length at different distances from the bearings, which points, +even with both girders loaded, deflect dissimilar amounts, and the +bracing will, if at one end attached near a rigid bearing, transfer some +part of the load from one girder to the other, notwithstanding that +both girders may be of the same span and equal extraneous loading. It +would not be difficult to ascertain the amount of load so transferred +from a consideration of the relative movements if free, and the loads on +the two girders necessary to render these movements equal, if the +deflections were simply vertical; but as there will be some twisting and +yielding of the girders on their seats, the calculation becomes +involved. If the bracing is placed at about the middle of the girders, +the effects noted will be greatly reduced; first, because the difference +of movements near the centre will be less; second, any given difference +will correspond to a smaller transference of load; and, third, because +each girder will there be more free to twist than at the ends. It +therefore appears that bracings between the girders of a skew bridge +should not be placed near the bearings, though they may be put, with +much less risk of injury, near the middle. + +Cross-girders on a skew bridge are subject to forces somewhat similar to +those which may affect bracing, rendering it desirable to design their +attachments in a manner which shall not aggravate the matter, but rather +reduce the effects of unequal vertical displacement of their ends where +secured to the main girders. + +Crossed flat bars as bracing members are objectionable on account of +their tendency to rattle, after working loose; but as this effect only +ensues in bracing which has first become loose (it being assumed that +the bars in any case are connected where they cross), this objection is +not itself vital, though greater rigidity is easily obtained by making +all such members of a stiff section. + +Defective bracing between girders, from neglect of the very considerable +forces it may be called upon to communicate, is very common; the writer +has seen many such cases, of which one is here illustrated in Fig. 26. + +[Illustration: FIG. 26.] + +This bridge, of the section shown, and 85 feet span, had very light web +structure. The bracings, of which there were two sets, were wholly +inefficient, the end rivets being loose in enlarged holes. Upon the +passage of a train there was a positive lurching of the girder tops from +side to side. The integrity of the bridge was really dependent upon +such stiffness as there was in the girders, and unplated floor. + +A common but indifferent method of keeping the top members of main +girders in line is by the use of overhead girders alone, frequently +curved to give the requisite clearance over the road. This cannot be +considered as wholly inefficient, as sometimes maintained, since it is +evident that the closed frame formed by the floor beams, the web members +of the main girders, and the overhead girder itself, must take a greater +force to distort it than would be necessary to cause deformation of a +corresponding degree, in an open frame formed by the omission of the +overhead girder; but it is not a method to be recommended, its precise +utility is difficult to estimate, and, if the cross-girder attachments +are of a rigid character, tends to increase the stresses induced at +those connections. The latter consideration is, however, not applicable +to this arrangement alone. All overhead bracing favours this by +restraining the tendency of the top booms to cant inwards when the floor +beams are loaded; and though this restraint may be quite harmless, it is +desirable that close attention be given to these effects in designing +bridges which make a complete frame more or less rigid in its character. +“Sway” bracing, sometimes introduced at right angles to the bridge +between opposite verticals, tends to emphasise these effects by +rendering the cross-section of the bridge still stiffer, besides making +it a matter of difficulty to ascertain how much of the wind forces on +the top boom is carried to the abutment by the top system of bracing, +and how much by the floor. The author does not, however, mean to suggest +that it cannot be used with propriety, but rather that extreme care is +desirable in considering its ultimate effect on the rest of the +structure. + +For girders of moderate depth there may be on these grounds a distinct +advantage in abandoning overhead bracing, and securing rigidity of the +top boom, and adequate resistance to wind forces, by making the +connection between the cross-girders and the web members sufficiently +good to insure, as a whole, a stiff [U]-shaped frame; but this, with the +ordinary type of rocker arrangement under the main girder bearings, will +not be entirely free from objection, as canting of the girders due to +floor loading will throw extreme pressure on the inner end of each +rocker. There appears to be no reason why the cylindrical knuckle should +not in this case be supplanted by a cup hinge, allowing angular movement +of the girder bearing in any plane. + +[Illustration: FIG. 27.] + +The efficient stiffening of light girders, as in the case of +foot-bridges, from the floor, where this is at the bottom flanges, +renders very narrow top booms permissible. This is a decided advantage +where lightness of appearance is aimed at; but it is not unusual to see +an attempt made in this direction by introducing gusset plates of very +ample proportions between vertical members of the girders, and the +projecting ends of flimsy transoms, carried beyond the width of the +bridge proper, these being of a section wholly out of proportion to the +brackets they are supposed to secure. Whatever may be the amount of +strength necessary at the point A, in Fig. 27, there should not be less +throughout the transom from one girder to the other. The degree of +strength and stiffness required in this member, and in the vertical +stiffeners is not, as a rule, great. Information to enable this question +to be dealt with as a matter of calculation is somewhat scanty; but it +would appear to be sufficient to insure safety that, for an assumed +small amount of curvature in the compression member, the forces outwards +corresponding to this curvature, due to thrust, should be resisted by +verticals and transoms of strength and stiffness sufficient to restrain +it from any further flexure. It will, of course, be necessary also to +take care that the compression member is good as a strut between the +points of restraint. A simple and sufficiently precise method of dealing +with this question is much needed. In cases where the floor weight rests +on the flange projection, it is also necessary to give the transom +additional strength to an extent enabling it to resist the twisting +effort between any two of these transverse members; further, resistance +to wind on the girder has to be provided in both transoms and verticals. + +It may be hardly necessary to insist that bracing intended to stiffen a +structure against wind, local crippling, or vibration, should be made +complete, not stopping short at some point, because it cannot +conveniently be carried further, as is sometimes done, unless the +strength of those parts of the structure through which the forces from +the bracing must be communicated to the abutments is sufficiently great, +considered with reference to other stresses in those parts which have +also to be endured. + +Bracing stopped short in this way, making only the central part of a +bridge rigid, may have the effect of increasing the forces to which the +unstiffened end members would otherwise be liable. Such a structure +would evidently be much stiffer against wind-gusts than if no bracing +existed--the resistance to a blow would be increased; but the power to +maintain that greater resistance being confined to the intermediate +bays, the unbraced ends would be subject to greater maximum forces than +if bracing were wholly omitted. The net effect may still be better than +with no bracing, the point raised being simply that of an increase of +stress in particular end members. + +In the bracing of tall piers, the rising members of which will be +subject to any considerable stress, if the diagonal members are not +finally secured when the piers are under their full load, or an initial +stress of proper amount induced in those members, the effect of loading +will be to render them slack; so that an appreciable amount of movement +at the top may occur before it can be limited by the efficient action of +the bracings. This effect under blasts of wind or continual passage of +trains may, indeed, be dangerous. Similar considerations apply to the +top wind bracing of deep girder bridges, influencing also the bottom +bracing in a contrary manner, which calls for attention in fixing the +unit stresses for such members. + +The bracing of sea-piers is very liable to slacken if made with +pin-and-eye ends, as is often done for round rods. The detail presents +advantages in erection, but is not altogether satisfactory in practice. +Such connections are continually working. In the finest weather, with +the sea quite smooth but for an almost imperceptible wave movement, the +lower parts of such structures will be found, as a rule, to have some +slight motion. This is very trying to bracing; nor is there room for +surprise when it is considered that these oscillations, occurring at +about ten to each minute, never wholly cease, and amount in the course +of one year to over five million in number. + +Bracing attached in such a manner that there can be no initial slack, or +slack due to wear under endless repetitions of small amounts of stress, +will have a much better chance to keep tight. The advantage presented +by round rods in offering little surface to the water, is more than +negatived by inefficiency of the usual attachments for such rods. + +The author has observed that bracing of members possessing some +stiffness, and with good end attachments to ample surfaces, appears to +stand best in ordinary sea-pier work. For such structures the bracing +should consist of a few good members, with a solid form of attachment, +rather than of a multiplicity of lighter adjustable members, which will +commonly give great trouble in maintenance; being very possibly also, in +the case of sea-pier work, in unskilled hands. If round rods must be +used, they will stand much better if made of large diameter. + +Before leaving the subject of bracing, it may not be out of place to +refer to wind pressure, as this may so much affect the proportioning of +the members. + +Some years since the author had occasion to examine a number of +structures with respect to their stability. Of foot-bridges from 60 feet +to 120 feet long, three or four, when calculated on the basis +recommended by the Board of Trade as to pressures upon open-work +structures, worked out at an overturning pressure of from 18 lb. to 22 +lb. per square foot. These bridges had been many years in existence; it +is, therefore, fair to assume that no such wind in the direction +required for overturning had expended its force upon them as to the +whole surface. + +[Illustration: FIG. 28.] + +Particulars were taken in 1895 of a notice-board, presenting about 12 +square feet of surface, which was blown down in the great storm of March +24 of that year, at Bilston, in Staffordshire. It was situated at the +foot of a slight slope, over which the wind came, striking the +obstruction at right angles. The board was mounted on two oak posts of +fair quality and condition, which broke near the ground at bolt holes +(see Fig. 28). The force required to do this, at 9000 lb. modulus of +rupture--a moderate value--corresponds to 50 lb. per square foot on the +surface exposed above the break. + +In the same neighbourhood, at the same time, considerable damage was +wrought in overturning chimney stacks, to buildings and roofs; the +general impression in the locality being that the storm was of +exceptional, even unprecedented, violence. Bilston, it should be noted, +lies high. + +At Bidston Hill, near Birkenhead, on the same occasion, a pressure of 27 +lb. was registered. In another part of the country it is said to have +been 37 lb. Wind is so capricious in its effects over small areas as to +render it probable that the maximum pressures have never been recorded; +but this is a matter of little importance where general stability and +strength only are concerned. The instances cited, though by themselves +insufficient to throw much light on the question, may be of use in +connection with other known examples. + + + + +CHAPTER V. + +RIVETED CONNECTIONS. + + +Considerable latitude is observable in the practice of engineers in the +use of rivets. Numberless experiments to determine the resistance of +riveted connections have from time to time been made, but these are not +to be considered by themselves as final, when the results of experience +in actual construction, are available for further enlightenment. + +The class of workmanship so largely influences the degree in which +rivets will maintain their integrity that it is only by the observation +of a large number of cases, including all degrees of workmanship, that +any reliable conclusions may be drawn. In this respect laboratory +experiments have an apparent advantage, as the conditions may be kept +sensibly the same; but, on the other hand, no such investigation +reproduces the circumstances of actual use, which alone must in the end +determine the utility of any inquiry for practical application. + +The author has studied the particulars of a number of cases to ascertain +under what conditions as to stress, having due regard to the effects of +vibration, rivets will remain tight, or become loose. Every loose rivet +that may be found cannot, of course, be taken as being due to excessive +stress; the more frequent cause is indifferent work, evidenced by the +fact that neighbouring rivets will frequently be found quite sound, +though the failure of some will cause a greater stress upon the +remainder. When rivets loosen as the direct result of over-stress, it is +usually by compression of the shank and enlargement of the hole, or by +stretching of the rivet and reduction of its diameter. Instances of +failure by partial or complete shear are extremely rare; indeed, the +author has never yet found one, though when a rivet has first worked +loose, as a result of excessive bearing pressure or bad work, it is not +uncommon to find it cut or bent as an after consequence. + +In estimating stresses at which rivets have remained tight, or loosened, +as the case may be, examples have generally been chosen in which there +could be no reasonable doubt as to the amount of those stresses by the +ordinary methods of computation. This is clearly most important, as, if +any appreciable uncertainty remained as to the degree of stress, the +results deduced would be of little value. For this reason those +instances in which the loads upon girders, or parts of girders, may find +their way to the supports by more than one route, are to be regarded +with caution, as are those in which full loading possibly never obtains, +but which may, on the other hand, perhaps have been frequent. The +working diameter of the rivet as it fills the hole has been used in +making the computations; in some cases from direct measurement from +particular rivets, in others with a suitable allowance for excess +diameter of hole, according to the class of work under consideration. + +Dealing first with main girders, it may be said that rivets attaching +the webs of plate girders to the flange angles rarely loosen, though +subject to considerable stress. In illustration of this may be named a +bridge for two lines of way, 85 feet effective span, having two main +girders with plate webs, and cross-girders resting on the top flanges, +previously referred to (see Fig. 26). + +The girders, which were 6 feet 9 inches deep, had a bearing upon the +abutments of 4 feet; the rivets were 7/8 inch in diameter and 4 inches +pitch. There is in a case of this kind some little uncertainty as to +what is the stress on the flange angle rivets at, or very near to, the +bearings; but, taking the vertical rows of rivets at the web joints near +the ends as presenting less uncertainty, the stress per rivet works out +at 4·8 tons, being 4 tons per square inch on each shear surface, and 11 +tons per square inch bearing pressure upon the shank in the web plate, +which was barely 1/2 inch thick. This bridge was frequently loaded upon +both roads, but with one road only carrying live load, the stresses in +the more heavily loaded girder would be fully 90 per cent. of those +obtaining as a maximum. There was on this bridge, which had been in use +31 years, considerable movement and vibration. + +It is by no means uncommon to find cases of rivets in main girders +taking 11 tons per square inch bearing pressure--occasionally more--and +remaining tight. As furnishing an instructive, though slightly +ambiguous, instance of rivets in single shear, may be cited a bridge not +greatly less than that just referred to, of about 65 feet span, carrying +two lines of way, there being two outer and one centre main girder of +multiple lattice type, with cross-girders in one length 4 feet apart, +riveted to the bottom booms of the main girders; these rivets, by the +way, were in tension. The floor was plated, the road consisting of stout +timber longitudinals, chairs, and rails (Fig. 29). + +[Illustration: FIG. 29.] + +It should be noted that there is in this case some difficulty in +ascertaining the precise behaviour of the cross-girders, affecting the +proportion of load carried by the outer and the inner main girders. +Strict continuity of all the cross-girders could only obtain if the +deflection of the main girders were such as to keep the three points of +suspension of each cross-girder in the same straight line. A close +inquiry showed that this was very far from being the case, and that +while each cross-girder at the centre of the bridge would, under load, +by relative depression of the middle point of support, be reduced to +the condition of two simple beams, those at the extreme ends of the span +would behave as continuous girders. + +With both roads carrying engine loads equal to those coming upon the +bridge, the author estimates that for the centre main girder the shear +on the rivets of the end diagonals, secured by one rivet only, was 14·9 +tons per square inch, and the bearing pressure 16·3 tons; the flange +stress being 7·1 tons per square inch net. The outer main girders are +most heavily stressed when but one road, next to the outer girder +considered, carries live load. For this condition the stresses work out +at 9 tons per square inch shear on the rivets of the end diagonals, and +9 tons bearing pressure, the flange stress being 5·7 tons per square +inch on the net section. + +Without intending to throw any doubt upon the substantial truth of these +results, it must be admitted that instances of greater simplicity of +stress determination are much to be preferred. For purposes of +comparison, but not as having any other value, the results have also +been worked out on the supposition of all cross-girders acting each as +two simple beams, and also for strict continuity, and are here +tabulated, together with the conclusions given above. + +The cross-girders were moderately stressed, and the tension on the +rivets attaching them to the main girders probably did not exceed 3 tons +per square inch. + +It should be pointed out that the traffic over the bridge was small. The +centre main girder but seldom bore its full load, though at all times +liable to receive it. Much importance cannot, therefore, be attached to +the results for this girder, other than as showing how a structure may +stand for many years, though liable at any time to the development of +stresses which would commonly be regarded as destructive, or nearly so. + +EXAMPLES OF RIVET STRESSES, ETC., IN LATTICE GIRDERS. + + ---------------------------------+-----------+------------+--------- + | Cross- | Cross- | + | Girders | Girders as | Correct + | as Simple | Continuous | Results. + -- | Beams. | Beams. | + +-----------+------------+--------- + | Stress in Tons per Square Inch. + ---------------------------------+-----------+------------+--------- + Centre girder, 63 ft. span (both | | | + roads loaded): | | | + Rivets in diagonals--Shear | 13·7 | 17·2 | 14·9 + Do. Bearing | | | + pressure | 15·0 | 18·8 | 16·3 + Flange | | | + stress | 6·8 | 8·5 | 7·1 + | | | + Outer girder, 66 ft. span (near | | | + road loaded): | | | + Rivets in diagonals--Shear | 9·6 | 8·2 | 9·0 + Do. Bearing | | | + pressure | 9·6 | 8·2 | 9·0 + Flange | | | + stress | 5·9 | 5·1 | 5·7 + ---------------------------------+-----------+------------+--------- + +The material and workmanship of the bridge were good. The rivets of the +centre girder end diagonals, 1 inch in diameter, were originally 7/8 +inch, but on becoming loose were cut out, the holes reamered, and +replaced by the larger size, which remained tight, and to which the +stress figures apply. The rivets in the diagonals near the centre, 7/8 +inch in diameter, which were subject to reversal of stress, occasionally +worked loose, and were more than once replaced. The riveting in the +outer girder diagonals, subject to smaller stresses, much more +frequently developed, also gave trouble, particularly those liable to +counter stresses. + +Apart from looseness of rivets, the general appearance and behaviour of +the bridge, which had been in existence about twenty years, was not +suggestive of any weakness. + +Of smaller girders, an example showing the necessity for care in +discriminating, if it be possible, between looseness of rivets resulting +from over-stress and that due to other influences may first be quoted. +Two trough girders, of 11 feet effective span, each of the section shown +in Fig. 30, 11-1/2 inches deep at the ends, 14 inches at the middle, +with 1/4-inch webs, and rivets 3/4 inch in diameter, of 4-1/2-inch +pitch, showed certain defects, of which one, it may be incidentally +mentioned, was a cracked web (Fig. 31). From the nature of the +arrangement the lower web rivets, which were loose, would receive the +first shock of the load coming upon the span, but there were evidences +indicative of original bad work. The angle bars gaped, suggesting that +these had first been riveted to the bottom plate, and left sufficiently +wide to allow the web to be afterwards inserted, the rivets failing to +pull the work close, and then readily working loose. Here there is +considerable uncertainty as to how much of the loosening is to be +attributed to bad work, and how much to stress. It may, however, be +remarked that whatever bearing stress was the ultimate result of the +load hammering on the lower angle flanges, loosening rivets never +perhaps really tight, the stress of 7 tons per square inch bearing +pressure on the upper rivets, though aggravated by considerable +impactive force, was not sufficient to loosen these. The girders were +taken out after being in place sixteen years. + +[Illustration: FIG. 32.] + +[Illustration: FIG. 30.] + +[Illustration: FIG. 31.] + +An instance of undoubted excessive bearing pressure was found in the +cross-girders of a bridge, mentioned on p. 15, of which so many web +plates were cracked. This bridge, carrying two lines of way, had outer +main girders, and long cross-girders with 1/4-inch webs and 3/4-inch +rivets, 4 inches pitch. The rivet stresses work out at 4·3 tons per +square inch on each shear surface, and 24 tons per square inch bearing +pressure. For one road only being loaded, the latter figure falls to +18·5 tons. The traffic over this bridge, twenty years old, was +considerable, rapid, and heavy. It is hardly necessary to add that a +large number of the rivets were loose, one of which is shown in Fig. 32. + +[Illustration: FIG. 33.] + +To take another case relating to a floor system of extremely bad design +(Fig. 33). The main girders were 11 feet apart, 35 feet span, the floor +having two cross-girders only, spaced at 11 feet 3 inches, and 9 inches +deep, supporting hog-backed trough longitudinals. The cross-girders were +at their ends but 6-3/4 inches deep, the distance from the bearing of +cross-girders to centre of longitudinals carrying a rail being 2 feet 10 +inches, in which length were eight rivets in the web and angles at the +top, and six at the bottom, all 3/4 inch in diameter. + +The shear stress on the upper rivets works out at 7·3 tons per square +inch on each shear surface, the bearing pressure 20·6 tons per square +inch. On the lower rivets the shear stress becomes 9·7 tons, and the +bearing pressure 27·4 tons, per square inch. Care was exercised in +computing these stresses, that part of the bending moment carried by the +web being allowed for, but it must be admitted that the result is, +probably, approximate only. The sketch here given shows the cross-girder +end and section. The rivets, though in double shear, were, as might be +expected, loose, notwithstanding that the traffic over the bridge was +moderate, and quite slow. The floor system was remodelled after twelve +years’ use. + +In illustration of the behaviour of rivets in the ends of long +cross-girders, both shallow and weak, and many years in use under heavy +traffic, may be cited connections having end angle bars to the +cross-girders, with six rivets through the web of main girders. The +bearing pressure worked out at 7·8 tons per square inch. Many rivets +were loose, but it should be remarked that the workmanship was not of +the best class, and the cross girders flexible: a characteristic very +trying to end rivets, and inducing a stretch in some, already referred +to as a possible cause of loosening. This will be apparent if the +probable end slope of weak girders be considered. The author concludes +that this inclination should not, for ordinary cases, exceed 1 in 250; +but the ratio must largely depend upon the degree of rigidity of the +part to which the connection is made. It is commonly regarded as bad +practice to submit rivets to tension, yet this is frequently, though +unintentionally, permitted in end attachments, without any attempt to +limit the amount of tension. With suitable restrictions, there appears +no serious objection to rivet tension for many situations. + +Another instance of cross-girder end connections of a different type is +illustrated in Fig. 34. + +The main girders of the bridge were 12 feet apart, each cross-girder end +carrying its share of the half of one road. The mean bearing pressure +upon the rivet shanks works out at 5·8 tons per square inch for the six +rivets of the original joint, but in the particular joint shown some of +the rivets had loosened, making the bearing pressure upon the remainder +about 8·7 tons per square inch. It is apparent there must have been +considerable stress on the top and bottom rivets which loosened. These +two rivets would also, because of difficult access, be in all likelihood +insufficiently hammered up. The joints worked rather badly; the loose +rivets had “cut” to a considerable extent, a process materially assisted +by the gritty nature of the ballast (limestone), particles of which, +getting into the joint, contributed to the sawing action; this had +clearly been taking effect for some considerable time. (See Fig. 35.) + +[Illustration: FIG. 34.] + +[Illustration: FIG. 35.] + +The two cases of cross-girder ends given are both rather exceptional in +character, and in each case the defects appear to be due to general bad +design and workmanship rather than to any serious excess of bearing +pressure. This may be illustrated by taking the common case of +cross-girders, 2 feet deep, carrying two roads, and having end angle +irons riveted to the web and stiffeners of the main girders by ten +rivets in single shear at each end. In this example, which is, for old +work, simply typical, and does not relate to any specific instance, the +bearing pressure on the rivets will work out at from 6 to 8 tons per +square inch, and will seldom be accompanied by looseness of rivets, and +then only as a result of faulty work. + +Some sketches of rivets taken from old bridges have already been given +in connection with the cases to which they belong; a few others are here +shown (Figs. 36 to 40) to further illustrate what may be the actual +condition of rivets after some years’ use, and how different from the +ideal rivet upon which calculations are based. These are, however, bad +instances. + +[Illustration: FIG. 36.] + +[Illustration: FIG. 37.] + +[Illustration: FIG. 38.] + +[Illustration: FIG. 39.] + +[Illustration: FIG. 40.] + +It should be noticed that rivets may, if in double shear, be loose in +the middle thickness, due to enlargement of the hole in the central part +and compression of the rivet, and yet show no sign of this by testing +with the hammer. There is, however, generally marked evidence of another +kind in the “working” of the inner part, as, for instance, the web of a +plate girder, in which case a discoloration due to rust is to be found +along the edges of the angle bars, or a movement may be detected on the +passage of live load. Red rust is, in fact, frequently an indication of +something wrong, when no other evidence is apparent. In plate girders +having [T] or [L] bars brought down and cranked on to the top of shallow +cross-girders, it is not uncommon to find the rivets attaching these +bars to the cross-girder tops loose, due to causes already dealt with. +The riveted connection should, as to strength, bear some relation to the +strength and stiffness of the parts secured, if the rivets are to remain +sound. + +It may be well to give here a summarised statement of the results +already named, for purposes of ready reference. These by themselves are +not sufficient to enable working stresses to be deduced, though they are +instructive. The author has found many instances of shear and bearing +stresses in excess of those usually sanctioned, under which the rivets +behaved well, but is not now able to give precise particulars of these. + +EXAMPLES OF RIVET STRESSES. + + ---------+-----+---------+------+------+--------+----------------- + -- |Span | Where |Shear |Single|Bearing | Tight or Loose. + | in | Found. |Stress| or |Pressure| + |Feet.| | in |Double|in Tons | + | | | Tons |Shear.| per | + | | | per | | Square | + | | |Square| | Inch. | + | | |Inch. | | | + ---------+-----+---------+------+------+--------+----------------- + Main {| 85 | Web | 4·0 | D | 11·0 | Tight. + girders {| 66 |Diagonals| 9·0 | S | 9·0 | Many loose. + {| 63 | „ | 14·9 | S | 16·3 | Tight generally. + | | | | | | + {| 11 | Web | 1·4 | D | 7·0 | Tight. + Small {| 26 | „ | 4·3 | D | 24·0 | Many loose. + girders {| 11 | „ | 7·3 | D | 20·6 | Loose. + {| 11 | „ | 9·7 | D | 27·4 | Loose. + | | | | | | + End {| 27 | Ends | 5·4 | S | 7·8 | Loose. + connec- {| 12 | „ | 1·8 | D | {5·8 |}Many loose. + tions {| | | | | {8·7 |} + | | | | | | + (Type | | | | | | + case) | 26 | „ | 4·8 | S | 7·0 | Tight. + ---------+-----+---------+------+------+--------+----------------- + +It is probable that the fact of a rivet being in single or in double +shear largely affects its ability to resist the effects of bearing +pressure, as commonly estimated. In the first case, the rivet-shank must +bear heavily on the half-thickness of the plates or bars through which +it passes, rather than on the whole thickness; and it is to be supposed +that under this condition it will work loose at a lower average stress +than if it were in double shear, and the pressure better distributed. + +[Illustration: FIG. 41.] + +[Illustration: FIG. 42.] + +The author has no very definite information in support of this +contention, but suggests that for double shear the permissible bearing +pressure may probably be as much as 50 per cent. greater than for rivets +in single shear; the difference being made rather in the direction of +increasing the allowable load on double-shear rivets, than in reducing +that upon rivets in single shear. The propriety of this is evident when +it is considered that the practice has commonly been to make no +distinction, so that whatever bearing pressures are found to be +sufficient for both cases may be increased for those capable of taking +the greater amount. Figs. 41 and 42, here given, illustrate the +behaviour of rivets under the two conditions. + +With reference to the amounts of the stresses to which rivets may be +subject, the author concludes, as a result of his experience, coupled +with a consideration of known laboratory tests, that for all dead load +these may be quite prudently higher than is frequently taken. For iron +the shear stress to be 10 per cent. less than the stress of parts +joined; and the bearing pressure--for single-shear rivets, 20 per cent.; +and for double-shear rivets, 80 per cent. greater. For ordinary mild +steel the shear stress to be 20 per cent. less than the stress in parts +connected, and the bearing pressure equal to it for single-shear rivets; +and 50 per cent. more for rivets in double shear, though the two latter +values may probably approach those for wrought iron in steel of the +higher grades sometimes used in bridge-work. For live load, or part live +and part dead load, the same rules may apply, the reduction of the +nominal working stress, arrived at by any one of the methods in use +which may be adopted, affecting both the parts connected, and the rivets +connecting them. For reverse stresses it is advisable to keep the shear +stress in any rivet so low, say 3 tons per square inch, that the +frictional resistance of the parts gripped by the rivets shall be +sufficient to prevent any tendency to slip under the influence of the +smaller of the two forces to which the part is liable, to insure that, +if brought to a bearing in one direction by the greater force, it shall +not go back with reversal of stress. This requirement may be open to +some question with respect to good machine-riveted work, but for +hand-riveted connections it may certainly be adopted with wisdom. + +The following table will show at a glance how the stresses proposed vary +with the unit stresses governing the main sections. + +PROPOSED TABLE OF RIVET STRESSES. + + -----------+-------------+----------------+---------------- + Unit Stress| |Bearing Pressure|Bearing Pressure + in |Shear Stress.|for Single-Shear|for Double-Shear + Member. | | Rivets. | Rivets. + -----------+-------------+----------------+---------------- + _Wrought Iron.--Tons per Square Inch._ + 3·0 | 2·7 | 3·6 | 5·4 + 4·0 | 3·6 | 4·8 | 7·2 + 5·0 | 4·5 | 6·0 | 9·0 + 6·0 | 5·4 | 7·2 | 10·8 + 7·0 | 6·3 | 8·4 | 12·6 + _Steel.--Tons per Square Inch._ + 4·0 | 3·2 | 4·0 | 6·0 + 5·0 | 4·0 | 5·0 | 7·5 + 6·0 | 4·8 | 6·0 | 9·0 + 7·0 | 5·6 | 7·0 | 10·5 + 8·0 | 6·4 | 8·0 | 12·0 + 9·0 | 7·2 | 9·0 | 13·5 + -----------+-------------+----------------+---------------- + + NOTE.--Tension on rivets to be limited to one-half the permissible + shear stress, the holes being slightly countersunk under snap-head. + +It may be objected that the shear stresses in the proposed table are +somewhat high for wrought iron and steel. This feature is intentional, +and is supported by the consideration that whereas there may be loss of +strength in the members of a structure by waste, there is no such loss +in rivets, if the work is so designed that there shall be no loosening. +Any allowance that may be desirable for loose or defective field rivets +is left to be dealt with as may be considered advisable for each +particular case, the table as it stands being applicable only to +riveting not below the standard of first-rate hand work. + +Cases of loose rivets in main girders over 50 feet span, due to any +cause but bad work, are extremely rare, unless resulting from the action +of some other part of the structure. It may be stated broadly that for +railway bridges of less than perfect design, the nearer the rail, the +more loose rivets, generally at connections. This is, no doubt, largely +due to the severe impact of the load, the effects of which are greater +near the rail, both because of the small proportion of dead load, and +because this effect has been but little modified by the elasticity of +any considerable length of intervening girder-work. In addition to this, +it is quite usual to find the rivets more heavily stressed, even though +the load be considered as “static,” in the floor system than in the +main-girders, though the reverse should be the case. It is unfortunate +that those parts which require the best riveting--viz., the +connections--are commonly dealt with by hand; and for this reason it is +the more necessary to design these with the greatest care. + +Any arrangement which favours the gradual acceptance of stress by one +part from another will contribute to the integrity of riveted +connections, and lessen the liability of the material to develop faults. +In other branches of design this is well recognised, but appears in much +old bridge work to have been entirely overlooked. + +Bridges carrying public roads very seldom furnish examples of loose +rivets; the conditions are generally much more favourable, impact being +practically absent, full loading infrequent, and the proportion of dead +load to live, high. + +It is, perhaps, hardly necessary to insist upon rivets being, apart from +mere considerations of strength, sufficiently near together to insure +close work and exclude moisture. Outside edge seams should never be more +widely spaced than 16 times the thickness of the plates; 12 thicknesses +apart is better. In the case of angle, tee, and channel sections, the +greater stiffness of the section makes wider spacing allowable up to, +say, 20 times the thickness; but this must be governed largely by the +amount of riveting required to pull the parts close together. Where more +than four thicknesses are to be gripped by the rivets, 3/4 inch in +diameter is hardly sufficient to insure tight work, and quite unsuitable +if the plates exceed 5/8 inch thick. + + + + +CHAPTER VI. + +HIGH STRESS. + + +High stress, provided it be well below that at which immediate injury +results, or possible failure, is not uniformly objectionable. It may be +first considered relative to the absolute and elastic limits of +strength, next with respect to the range of stress, and, finally, with +regard to the frequency of application. For practical purposes--that is, +for the continued efficiency of a structure--the limit of elasticity +must be considered to be the limit of strength, or, more strictly, the +limit for all those parts of the structure which must, so long as it +lasts, be liable to the original measure of stress. There may be places +in a bridge, however, over-stressed only in the earlier period of its +existence, which, by being over-stressed and suffering deformation, +permit the origin of this distortion to be harmlessly met in some other +way. In such a case the injury done to that part does not, of necessity, +lead to any culminating disaster; indeed, were it not for this +plasticity it is probable a large number of bridges would fail after +being in use but a short time. As for riveting, so in dealing with the +amount of stress to which a member is supposed to be liable, it should +be clearly understood by what method this has been arrived at, whether +the value assigned is the actual measure of the stress, or simply the +conventional amount arrived at in the conventional way; perhaps +neglecting web section in plate girders, or without regard to the +various influences which may reduce or increase the nominal amount of +stress, or including only a partial recognition of those influences. In +any case quoted the stress named is that at which the author arrives by +the ordinary methods of computation carefully applied, where these +appear to be sufficiently precise, unless any qualifying remark be +added. Extreme flange stress is in special cases computed, first on the +gross section by estimating the moment of inertia on that basis, and +deducing the stress at the holes from the ratio of net to gross section +at the extreme fibres; a method more correct than by reference to the +moment of inertia of the net section. Any exhaustive refinement in the +study of stresses is not attempted, both because it is beyond the +author’s powers of analysis, and for the reason that such results are +not comparable with the results of ordinary methods of calculation in +practice. Effective spans are taken at moderate values, and all +exaggeration is avoided. + +The effects of impact in any part vary so much with nearness to, or +remoteness from, the living load, and the frequency of development of +the maximum stress from all causes acting together is so much affected +by the same consideration, that it is apparent a nominal stress which +may be harmless in one part of a bridge may be destructive in some +other, a statement borne out by observation. Stress, as ordinarily +stated--i.e., at so much per square inch, uniform across a section--is +seldom a cause of trouble. In nearly all cases of failure there is an +accompanying localised destructive stress, either in rivets or +elsewhere, with crippling or deformation of some essential part. In the +tension flanges of main girders with uncomplicated stress, this may run +up to an amount very considerably beyond the ordinary limits without +producing signs of distress. The same remark applies to the compression +flanges, if these be in themselves sufficiently stiff, or properly +restrained from side flexure. In support of the above statement may be +quoted the following instances relating to wrought-iron structures:-- + +A bridge of 60 feet effective span, having girders immediately under the +rails, had a flange stress of 6·3 tons per square inch. Another of 64 +feet span, carrying two lines of way, with outside main girders and +cross-girders, had the flanges of the former stressed to 6·8 tons per +square inch. A third, of 76 feet span, of similar construction to the +last, was stressed in the main girder flanges to 7·5 tons per square +inch. The webs were not included in the computation; the figures, +therefore, compare with ordinary practice. In these three cases the main +girders showed no signs of distress, referable to the results stated, +though the top flanges in the last case were curved inwards. The effect +of this flexing of the flange would be, of course, to increase the +amount of compressive stress along one edge, though to what degree +cannot now be stated. + +[Illustration: FIG. 43.] + +[Illustration: FIG. 45.] + +[Illustration: FIG. 44.] + +A further instance of considerable flange stress occurred in a bridge of +seven nearly equal continuous spans, 25 feet generally, the end and +greatest span being 29 feet 6 inches, centre to centre of bearings. Some +details of the bridge are given in Figs. 43 to 45. The four inner main +girders under rails were 2 feet deep, with webs 1/2 inch thick over +piers, and 3/8 inch at abutments, having flanges of two [L] bars, 3 +inches by 3 inches by 5/8 inch. There were also two outer girders of the +same depth, with single [L] bars. Plate diaphragms of full girder depth +and particularly stiff were carried right across the bridge at the +centre of the spans, and over the piers. The girders, though evidently +designed to be continuous, had very poor flange joints at each bearing, +of little more than one half the flange strength (see Fig. 45). It is +doubtful if the girders acted with strict continuity for long after +erection, as the excessive stress in the rivets of the flange joint +would, for that condition, have been nearly sufficient to shear them. It +is probable that this being so, the joints first yielded, relieving the +bending moment over the piers, and increasing it near mid-span. Whether +the end spans be considered as strictly continuous with the rest, or as +simple beams, the maximum bending moments would not greatly differ, +though occurring for continuity over the pier, for free beams at the +centre. There is, however, an intermediate condition which makes the +moments at these two places less than either maximum, but equal to each +other; a condition of semi-continuity agreeable to a partial efficiency +of the joints referred to. It is this state which has been calculated, +giving the minimum stress value that can be accepted. The diaphragm has +been assumed to transfer to the outer girders a due proportion of the +load. With this explanation it may now be stated that, under engine +loads corresponding to those running, the flange stress worked out at +7·4 tons per square inch tension, web included, or 9·7 tons per square +inch without considering the web; which stresses, it is more than +probable, may have been greater. The figures include the consideration +of anything which may contribute to lowering the stress, and are hardly +to be compared with those worked to in ordinary design of new work, in +which it would be quite usual to neglect the assistance of the outer +girders and the webs, to work to heaviest engine-loads, and possibly +include an allowance for the effects of settlement. Dealt with in this +way the girders would seem to be of about one-fourth the strength that +would be required in the design of a new bridge, in which certain +elements of strength would be deliberately ignored. + +The ironwork was in good condition, there was no ordinary evidence of +weakness apart from the calculated results, the vibration was distinctly +moderate, and the deflection, though not recorded, was certainly small. +The bridge did, indeed, seem somewhat inert under load, and favours a +suspicion, the author entertains, that old girderwork long overstressed +may have a sensibly higher modulus of elasticity than newer work at more +moderate stresses. The traffic was not very considerable, and both +roads, of the same spans, but seldom loaded at the same time; though +with this construction of bridge there would in either case be very +little difference. The author recalls no reason for supposing that the +piers had yielded in any sensible degree. The bridge was rebuilt after +some thirty-six years’ use. + +Stress of considerable amount in the flanges of a latticed main girder +of 63 feet span has already been noticed in the chapter on “Riveted +Connections,” which for the tension boom worked out to 7·1 tons per +square inch, the flanges in this case showing no signs of weakness. An +instance has also been given in dealing with a case of side flexure in +which the extreme fibre stress was calculated to be 10 tons per square +inch, the girder recovering its form when relieved of load. + +As to stress in cross-girder flanges, an example may be quoted of a +bridge of 109 feet span, carrying two roads, having outside main +girders, with cross-girders between; these latter were stressed in the +flanges to 6·7 tons per square inch (webs not included), if the partial +distribution among the girders (which were spaced 6 feet apart) by the +rails and longitudinal timbers be neglected. There is some reason to +think in this instance that distribution had the effect of reducing the +stress quoted, as the observed deflection of the cross-girders was +materially less than that calculated for girders acting independently of +each other, though this may be in part due to a cause already hinted at. +Rigidity of the cross-girder ends, where attached to the heavy main +girders, would also tend to moderate the stress. No very definite +conclusion can therefore be deduced from this instance. + +To take another case of less uncertainty, the bridge of 35 feet span +(see Fig. 33), referred to in “Riveted Connections,” may again be cited. +The extreme fibre stress in the cross-girder flanges worked out at 6·3 +tons per square inch, web included, or 6·5 tons, exclusive of the web. +It cannot be said in this example that the girders showed no signs of +weakness, as the deflection under live load was 1/2 inch on the span of +11 feet, in addition to a permanent set of 3/4 inch, largely due, +however, to “working” rivets. + +A better and altogether conclusive case of the way in which +cross-girders may occasionally suffer considerable stress, and show no +sign, is furnished by two cross-girders, of which some particulars are +here given. These girders occurred in the floor of a very acute angled +skew bridge, riveted at one end to the main girders in a manner which +was very far from fixing the ends, resting at the other end on a masonry +abutment. The first girder was about 19 feet effective span, 12 inches +deep in the web, with angle bar and plate flanges. The girders were +spaced 6 feet apart, and were connected under the rails by [T]-bars, +cranked down to face the webs, and riveted through. Though these [T]’s +had little stiffness, yet the frequent vertical movements of the girders +relative to each other, under passing loads, had broken the majority of +the [T]-bars at the bends, so that no notice need be taken of these as +transferring load from any one cross-girder to its neighbour. The floor +covering consisted of timbers about 4 inches thick, also incompetent to +transfer any sensible proportion of the load on a girder to others 6 +feet distant. Upon the floor was cinder ballast, with sleepers, chairs, +and ordinary bull-headed rails. The stress to which the girder was +liable works out at 8·4 tons per square inch, on the extreme fibres of +the net section, web included; or 9·1 tons, neglecting the web, under +engine-loads of a common amount. The other girder had an effective span +of about 22 feet, as before 12 inches deep in the web, with angle bar +and plate flanges. The stress per square inch was 10·5 tons, web +included, or 11·1 tons per square inch, neglecting the web. This girder +carried three rails, one of which was near to the abutment bearing, so +that there was no great difference in the stress induced whether all +three rails were loaded or the pair only. The traffic over the bridge +was very great, but of moderate speed. It must have been a common +occurrence for the girders to take the full loads. The heavier engines +passed scores of times in a day--lighter engines probably one hundred +times. The bridge was about twenty years old, yet these cross-girders, +when removed, showed no other sign of age and wear than that due to +rust. + +[Illustration: FIG. 46.] + +All the foregoing instances relate to wrought-iron bridges. Two cases of +steel construction are here added, the first of these furnishing an +example of high girder stress somewhat remarkable. This was found in a +trough girder of a strange pattern, of which a section is here given +(Fig. 46). The bridge to which it belonged carried a siding, over which +engines of less than the heaviest class sometimes passed at a crawling +pace. The larger of the two girders carrying the rails was 15 feet 8 +inches effective span. The sides of the trough consisted each of two +vertical plates, originally 1/2 inch thick, but wasted to an aggregate +thickness of 5/8 inch. These plates 6 inches deep, were connected at +their lower edges to angle bars, 3 inches by 3 inches by 1/2 inch, which +again were riveted to a bottom plate 16 inches wide, originally 1/2 inch +thick, wasted to 3/8 inch. Lying in the bottom of the trough, and +riveted through the inner angle flanges, was a bridge-rail. Assuming +that the metal retained its elastic properties from top to bottom of the +section, at whatever stress, this works out at 32 tons per square inch +at the extreme top fibre, and 15 tons at the bottom, on the net section. +As puddled steel, of which the girders were made, may have a tenacity of +45 to 55 tons per square inch, the assumption is probably correct. The +author has no record of the deflection, but it may be remarked it was +such that to stand under the girder, with a tank engine passing over, +required some determination. + +A point of additional interest in this little bridge is that, though +made of steel, it dates as far back as 1861, having been in use +thirty-two years when removed. The particular variety of steel used was +known as Firth’s puddled. The evidence of this consists in +correspondence showing that permission had been asked of the controlling +authority, by the only users of the siding, to apply this material, with +no evidence of any refusal. At about the same time this steel was also +used upon the railway concerned in the top flanges of some girders of +considerable span. The appearance of the trough girders to which the +foregoing particulars apply was distinctly different to that which might +be expected in ordinary wrought iron. The top edges of the vertical +plates were wasted away, smooth, and rounded in a manner strongly +suggestive of a steely character. Finally, the way in which the girders +held up to their work for so long is, by itself, conclusive on the +point. The bridge-rail appeared to be of wrought iron, the different +modulus of elasticity of which has been included in the calculation upon +which the preceding results are based. That these girders stood so well +is, perhaps, largely due to the fact that the load carried by them was, +though varying within wide limits, practically free from impact, which, +had the load passed over quickly, would, with girders so small, shallow +and flexible, have been very sensible. + +The second instance of steel construction in which somewhat high stress +is manifest is that of some steel troughing of the Lindsay pattern, used +in a bridge built in 1885. The troughs ran parallel to the rails, having +an effective span of 18 feet 8 inches. The depth of the section (which +is shown in Fig. 47), was 8-1/2 inches, making a ratio of depth to span +of 1/28. The road was of ballast, sleepers, chairs, and 85-lb. rails. + +[Illustration: FIG. 47.] + +Assuming this to be carried on six troughs, which corresponds to 11 feet +3 inches of width, the extreme fibre stress works out at 7·5 tons per +square inch, under usual engine-loads. The bridge when examined after +fourteen years’ use was in good condition, and at that time but little +rusted; but the end seam rivets were, as is not uncommon with such +troughing, loose. The traffic over the bridge was considerable, but not +at great speed. + +On the opposite page are set out the results which have been given, in +tabulated form, as was done for rivet stresses, to enable ready +comparison to be made. + +EXAMPLES OF HIGH STRESS. + + --------------+-----+---------+---------------+--------+----------- + |Span | Part | Stress per |Tension |Condition. + | in |Stressed.| Square Inch. | or | + |Feet.| +-------+-------+Compres-| + -- | | | Webs | Webs | sion. | + | | | In- | not | | + | | |cluded.| In- | | + | | | |cluded.| | + --------------+-----+---------+-------+-------+--------+----------- + Wrought-iron | | | | | | + main girders, |60·0 |Flange | .. | 6·3 |Tension | Good. + plate | | | | | | + | | | | | | + Wrought-iron | | | | | | + main girders, |64·0 | „ | .. | 6·8 | „ | Good. + plate | | | | | | + | | | | | | + Wrought-iron | | | | | | + main girders, |76·0 | „ | .. | 7·5 | „ | Fair. + plate | | | | | | + | | | | | | + Wrought-iron | {| „ | 7·4 | 9·7 | „ |} + main girders, |29·5{| „ | 6·3 | 8·3} |Compres-|}Good. + plate | {| | | } |sion |} + | | | | | | + Wrought-iron | | | | | | + main girders, |63·0 | „ | 7·1 |Tension | Fair. + lattice | | | | | | + | | | | | | + Wrought-iron | | | | | | + main girders, |47·0 |Flange | 10·0 | .. |Compres-| Fair. + plate | |edge | | |sion | + | | | | | | + Wrought-iron | | | | | | + cross-girders,|26·0 |Flange | .. | 6·7 |Tension | Fair. + plate | | | | | | + | | | | | | + Wrought-iron | | | | | | + cross-girders,|11.0 | „ | 6·3 | 6·5 | „ | Bad; loose + plate | | | | | | rivets. + | | | | | | + Wrought-iron | | | | | | + cross-girders,|19·0 | „ | 8·4 | 9·1 | „ | Good, but + plate | | | | | | rusted. + | | | | | | + Wrought-iron | | | | | | + cross-girders,|22·0 | „ | 10·5 | 11·1 | „ | Good, but + plate | | | | | | rusted. + | | | | | | + Steel trough | {| „ | 15·0 | „ |}Fair, + girder |15.7{|Top edge | 32·0 |Compres-|}but + | {| | | |sion |}rusted. + | | | | | | + Steel |18·7 |Flanges | 7·5 | .. |Tension | Fair, + troughing | | | | |and Com-| but + | | | | |pression| rusted. + --------------+-----+---------+-------+-------+--------+----------- + +It would be unwise to infer from the instances which have been quoted +that high stress may be regarded with complaisance. In the most +conscientious engineering work there should still be a liberal margin +for material possibly defective, or even bad, for waste and +deterioration, and for the aggregate effect of minor errors in design, +any one of which considerations, except the first, by itself might not +be of great importance. The conclusion which may, however, be derived +from this and the previous chapters is, that bridge failures are less +likely to occur from high stress of a kind readily calculated than from +failure in detail, obscure and little suspected, the reason for which is +not perhaps apparent, till the attention is forcibly directed to it by +the refusal of the structure to sustain the forces to which it may be +liable. + + + + +CHAPTER VII. + +DEFORMATIONS. + + +Instructive lessons are to be had from a study of the various +alterations in form to which metallic bridgework is liable, which +alterations may be due simply to the development of stress of ordinary +amount, and are then generally small; or to abnormal stresses, the +result of some distortion in the bridge structure itself not originally +intended, and possibly extreme. In addition to these there may be +deformations due to settlement, to “creeping” of parts of the structure +relative to the rest, to temperature changes, to rust, and to original +bad workmanship. In any instance quoted below the methods adopted to +ascertain the amounts of such alterations were quite simple, even crude; +but as care was exercised, and no attempt made to measure any very +minute changes, the results may be accepted as practically correct. + +Dismissing for the present changes of form such as are to be expected, +and touched upon in other places in this work, with respect to the +particular parts of bridge structures affected by them, a few instances +will be adduced of alterations which, though not very surprising, are +such as in the design of the work are hardly likely, in most instances, +to have been contemplated. + +A case has already been referred to in which, owing to eccentric loading +of main girders, these were, as to the top flanges, flexed sideways a +considerable amount. It is proposed to supplement this by further +remarks relative to somewhat similar cases. A like effect is frequently +to be observed in trough or twin girders, in which the rails are +supported upon longitudinal timbers resting upon projecting ledges +formed by the bottom angle-bars of such troughs. In old forms of this +arrangement it is common to find the two girders forming the trough +connected only by bolts passing through the timbers, or just above them +and below the rails; or connected by narrow strips, which serve no other +purpose than to prevent the sides spreading at the bottom. The top +flanges in such cases commonly curve inwards on the passage of the +running load, accompanied of necessity by an increase of compressive +stress upon the outer edges of the flanges, and perhaps by the working +of any flange-joint which may exist. This, both as to flexing of the top +flange and the working of a joint, was noticed in the case of a bridge +twenty-three years old, very similar to that illustrated in Figs. 8 and +9, and described on pages 13 and 14. The top flange consisted, however, +of a bridge rail riveted to the top edge of the web, butting at a joint, +and covered by thick cover strips (see Fig. 48). The joint itself was +poor, and depended largely upon the character of the butt, which was not +sufficiently good to prevent the top member kinking at this point, under +the joint influence of transverse effort and compressive stress, with +possibly some help from bolts passing through timber and webs, though +these being loose, the author does not think them at all responsible. +Although not strictly relevant, it may be remarked in passing that it is +very objectionable to use bolts as was done in this instance; for as the +timber settles down on its seat, taking the bolts with it, these bear +hard in the webs, enlarging or even, as in this case, tearing the holes, +accompanied by injury to the bolts themselves. The practice is now +almost obsolete, but the example is instructive as showing the +impropriety of securing timbers by bolts passing through them at right +angles to the action of the load, unless these bolts are quite free to +move with the timber as it compresses. + +If trough girders must be used, the better plan is to connect the two +sides by a continuous bottom plate, the trough thus formed being +properly drained, if the timber is not bedded in asphalt concrete; or to +introduce stiff diaphragms at intervals beneath timbers, if the depth +suffices. + +In the case just quoted the curvature of the top members of the girders +was inwards, but in the instance given below, of twin girders 26 feet +effective span, with longitudinal timbers between, resting, as before, +upon the inner ledge formed by the bottom flanges, the curvature was +observed in three out of four girders to be 1/2 inch in a contrary +direction, the fourth remaining straight. + +[Illustration: FIG. 48.] + +[Illustration: FIG. 49.] + +An inspection of the accompanying section, Fig. 49, will, perhaps, +render the reason evident when it is noticed that the top members are +very unsymmetrical in form, the effect of this being to give these +members, under stress, a strong tendency to flex outwards, apparently +more than sufficient to counteract the tendency of an eccentric +application of load on the bottom flange to bring them inwards. It is to +be observed that the eccentricity of the flange appears to be not +materially in excess, and is actually so, only because the thinness of +the web--1/4 inch--renders it incompetent to keep the bottom flange up +to its work, and so secure the full effect of the eccentric loading in +limiting the outward tendency, due to the section of the top member, +the effects of which are thus more apparent than would have been the +case with a stiffer web. Ties across from one bottom flange to the other +prevent the want of symmetry noticed in these--which, by the way, is on +the wrong side for utility--from having any particular effect. + +To give one other example of the consequences of eccentric loading, a +bridge of 48 feet effective span may be quoted. This bridge carried four +lines of way supported by five main girders, trussed by kicking-struts +in such a manner as to form a bastard arch. A part section and plan are +given in Figs. 50 and 51. + +[Illustration: FIG. 50.] + +[Illustration: FIG. 51.] + +The floor consisted of Lindsay’s troughing resting upon the lower +flanges of the main girders, the three middle girders, subject to +eccentric loading, sometimes on one side, sometimes on the other, were, +with dead load only, straight; but the two outer girders, liable to +loading only on one side, had, under repeated applications of such a +load, assumed a permanent curve towards the rails--13/16 inch in one +case and 1 inch in the other--which curvature, no doubt, increased when +a live load came upon the contiguous roads, though this was not +measured. It should be remarked in passing that, owing to settlement and +the canting of the abutments, the three middle girders were also +“down”--in one case 3/4 inch. The girders, with one near road loaded, +deflected 1/8 inch--greatly less than would have been the case had the +main girder not been trussed. The bridge, at the time these particulars +were obtained, had been in existence six years. + +Deformations due to settlement may be very considerable. The author +recalls two instances affecting continuous girders. In the first of +these, a bridge twenty years old, of two spans of about 50 feet each, +and with girders 4 feet 6 inches deep, the centre pier had sunk 4 +inches, reducing the spans, as respects the dead load, practically to +the condition of simple beams, just resting, but hardly bearing, upon +the piers when free of live load. + +In the second case, also of two openings of about 55 feet each, with +girders 8 feet deep, one abutment had sunk about 3 inches, more than +doubling the stresses over the centre pier. It is manifest that +continuous girders should only be adopted where settlement of the +supporting points is not likely to occur to any material degree. If this +cannot be relied upon, the theoretical flange sections may hardly be +worked to with any prudence; it being then advisable to make a liberal +allowance for settlement stresses, in which case any economical +advantage that should exist will probably disappear. It is, however, to +be acknowledged that so long as the girders are in touch, under dead +load, with the bearings intended to support them, the stresses due to a +live load are unaltered, the principal effect in this case being that +the variation in stress due to the live load ranges between limits that +are higher or lower in the scale of stress than is the case with +bearings undisturbed; still, if it is desired that the maximum stress +shall not exceed, say, 6 tons per square inch, it can hardly be a matter +of indifference that settlement shall induce a maximum of, perhaps, 10 +tons, as in that case the stress must be 4 tons nearer the limit of +statical strength. + +Before leaving this matter it may be well to point out that in the case +of continuous girders of uniform section a moderate settlement of the +piers may even be advantageous by reducing the moments over the piers, +and possibly making them equal to those obtaining near the middle of the +spans, in which case there will be less inequality of stress in the +booms and a reduction of the maximum stress. + +Bridges consisting of simple main girders connected by cross-girders may +be very prejudicially affected by unequal settlement; for instance, if +one girder bearing settles more than the others, a twist is put upon the +structure very trying to the floor-girder connections, and possibly to +the main girders; to the web if a plate girder, or to the verticals if +an open-webbed truss with rigid cross-girder attachments. Indeed, +settlement of this kind may be much more destructive to a metallic +bridge than to an arch of brick or masonry, the commonly accepted +opinion notwithstanding. + +Instances of deformations due to the creeping of some part of the +structure away from its work, are within the author’s knowledge, rare; +except in the case of the ends of main girders in skew bridges, already +referred to. + +Distortion, the result of temperature changes, is frequently to be +observed in any considerable length of girder flange or parapet where +there is not freedom of movement, unless due provision is made to check +it. + +It is quite common to see parapets out of line, either because the ends +are not free, or because the light work of the parapet being more +exposed to the sun’s rays than the girder work to which the lower part +is attached, expanding to a greater degree, is subject to considerable +compressive force, and buckles under its influence. The cure for this +condition is obviously to provide such parapets with free or flexible +joints at moderate distances apart, or to make the parapet sufficiently +stiff to take the stresses developed, without crippling. A parapet may +also go out of shape if directly attached to the top flange of a girder +liable to heavy loading, particularly if the girder be shallower than +the parapet, simply by its inability to maintain truth of line under the +compressive stress, which it shares with the top flange of the girder +proper. + +Rivets spaced too far apart, by allowing the plates or other parts to +spring open slightly, and permitting moisture to enter, results in the +growth of rust, which, as it swells in forming, forces the parts +asunder, and may set up considerable stress. + +Flat bars riveted together by rivets spaced 12 inches apart may from +this cause be forced asunder, as much as 1/2 inch, sufficient to set up +a stress, with any practicable thickness of bar, much exceeding the +elastic limit. + +Local distortions may occur as the result of imperfect workmanship or +careless erection, causing quite possibly very severe local stresses; or +girder flanges may be out of straight as a result of riveting up along +one side first, instead of advancing the riveting simultaneously along +the whole breadth of the flange. The injury done by drifting is well +known, and there is reason to think considerable damage is sometimes +done to girderwork during manufacture by rough treatment to make the +work come together; but the author has little to offer with respect to +these matters that is not common knowledge. It may, however, be pointed +out in passing that a bridge upon the design of which great care has +been expended, with the idea that theoretical propriety shall not be +violated, may be completely spoiled in this respect by careless +construction. Fortunately, both steel and wrought iron, if of good +quality, are long suffering. Incompetent erection will sometimes result +in the true girder camber not appearing, or in differences as between +girders supposed to be similar. This is not, of course, a deformation in +the sense in which the word has previously been used, but it is +desirable to bear the fact in mind as a possible cause of defective +camber in dealing with questions of deformation. + +The foregoing has reference chiefly to alterations of form in bridgework +of wrought iron or steel, but a case of considerable interest is that of +a cast-iron arched structure, of which the author made a very complete +examination. + +[Illustration: FIG. 52.] + +[Illustration: FIG. 53.] + +This bridge, built in 1839, and carrying two lines of railway, consisted +of three spans, 100 feet each, of 10 feet rise, made up of four inner +and two outer ribs, each rib being in three nearly equal parts; the +floor was of timber, the abutments and piers of masonry. As originally +constructed there was no bracing between the ribs other than the frames +indicated on the plan here given (Fig. 52), stretching from outer rib +to outer rib in the neighbourhood of the rib joints, which were simple +butts without bolts or any equivalent means of connection. The floor +was, however, braced in the horizontal plane, and the structure was also +braced over the masonry piers. After forty-two years’ use supplementary +distance-pieces were introduced between the ribs, but still no bracing +between them, or any efficient means of checking lateral movement. A +crack developing in one of the outer ribs at the crown, led to an +investigation to trace the cause, the bridge then being fifty-four years +old. Careful plumbing of the abutments revealed the fact that three out +of four abutment pilasters were out of the vertical, as shown in Figs. +52 and 53, the greatest amount being 5/8 inch in 6 feet--at that corner +from which the cracked rib had its springing; there was also other +evidence of settlement in an old crack extending from the top of the +abutment to the ground level, although this movement was very old, +certainly as to the greater part. The ribs of this span were also out of +plumb, that which was cracked being 2-1/2 inches out at the centre. The +joints of the ribs, which, as already stated, were simple butts, in some +cases opened and shut, as the load passed over, in such a way as to +suggest that the ribs were acting, in a manner, as four-hinged arches, +of which two hinges were at the springing, and the other two at the +joints, one of which would for most positions of the load be out of use, +reducing the rib to the three-hinged condition; in other words, as the +rolling load passed over the span, one or other of the two joints of a +rib would “gape” an appreciable amount at the bottom or at the top. +Observations were taken by means of a theodolite placed below, either +upon the bank or upon the tops of the masonry piers, sighting upon +suitable scales attached to the ribs to ascertain the amounts of +vertical and horizontal movement during the passage of trains over the +bridge. The principal results are set forth in the following table:-- + +MOVEMENTS OF CAST-IRON RIBS UNDER LIVE LOAD IN A BRIDGE OF THREE 100-FT. +SPANS. + + ----------------------+-------+----------+----------- + |Fall in| Rise in | Lateral + -- |Inches.| Inches. | Movement + | | |in Inches. + ----------------------+-------+----------+----------- + _Span No. 1._ + At A. Up road loaded | ·20 | ·08 | ·04 + „ A. Down road loaded| ·08 | ·03 | ·04 + „ B. Down road loaded| ·14 |No record.| ·02 + _Span No. 2._ + At C. Up road loaded | ·40 | ·13 | Slight. + „ C. Down road loaded| ·10 | ·05 | „ + _Span No. 3._ + At D. Up road loaded | ·22 |No record.| No record. + „ D. Down road loaded| ·15 | Slight. | Slight. + ----------------------+-------+----------+----------- + + NOTE.--The lateral movements are to either side of the mean position. + +The particulars for spans 2 and 3 were obtained with the instrument set +up on the pier between these spans. The tremor of this pier was such +that no useful readings for lateral movement could be obtained. Further, +as the rolling load came upon these spans, the effect was to rock the +pier to an extent vitiating the readings for vertical displacement; but +by sighting upon the fixed abutment, and observing the amount of this +rocking, suitable corrections were made in the apparent rib movements. +The figures given in the table are thus corrected. The pier rocking was +equivalent, as an extreme, to an inclination from the vertical of 1 in +3200. An attempt to measure the horizontal movement of the pier-top was +unsuccessful, owing to the impracticability of setting up the instrument +in a suitable position, sufficiently near to the pier to enable readings +to be satisfactorily taken. This horizontal displacement probably +amounted to about 1/16 inch either way. The rise and fall of the arches, +and rocking either way of the piers, varied, as might be expected, in +accordance with the position of the running load with respect to the +spans. Summarising the results, the greatest vertical movements +downwards were 0·20 inch, 0·40 inch, and 0·22 inch for spans Nos. 1, 2, +and 3, the upward movements being 0·08 inch and 0·13 inch for the first +and second spans, there being no recorded result of this kind for the +third span. With adjacent ribs loaded, the movement of the ribs unloaded +was one from one-third to one-half of the full amounts. It is to be +noted that the lateral displacement in no case exceeded 0·04 inch either +way, nor were the vertical movements exceptional; yet, as a matter of +sensation, when seated upon the ironwork, it was a little difficult to +believe them really so moderate. Observations were also made to +ascertain the rise of the arches from winter to summer temperatures, +with the result that this was found to be 0·45 inch, 0·45 inch, and 0·55 +inch for the spans in order, the extreme temperatures being fairly +representative of the English winter and summer. The structure was, as a +consequence of the examination, efficiently braced by diaphragms between +the ribs, and diagonals following the arch ribs round from springing to +springing, with satisfactory results. The crack already referred to, and +its probable causes, will be dealt with under “Cast-Iron Bridges.” +Eventually this bridge was reconstructed to meet the requirements of +growing engine-loads. + + + + +CHAPTER VIII. + +DEFLECTIONS. + + +Deflection, considered only as a fraction of the span, and without +regard to other conditions affecting it, is of very little use as an +indication of a girder’s fitness for its work; but when taken with +reference to the depth of the girder, the nature and amount of the load +producing flexure, and, further, with regard to the quality of the +workmanship and normal properties of the material of which the beam is +constructed, it may be of some little service in helping to form a +reliable opinion. This consideration applies with less force, perhaps, +to new work than to old, in which there may be unknown influences at +work, or unknown defects which by excessive deflection may be betrayed. +Though too much importance should not be attached to results of +deflection tests in any one instance, yet the practice of observing such +movements, and considering them with reference to each case, gives a +good general idea of what may be expected in a fresh instance, any +material departure from which should be a reason for specific inquiry as +to the cause. A further reason with new work is found in the evidence it +affords as to whether the loads carried travel to the supports really as +intended, or by some route not contemplated; or, in the case of floor +beams, in what way the load is distributed amongst them, if, indeed, +there be any such distribution. + +The author has commonly found that new work gives greater deflections +than old--i.e., while calculation gives the same result for each, it +does not apply equally well to both. The differences may be accidental, +but are probably due to other causes, perhaps to the fact that new work +has not by repeated applications of load lost the resilience of parts +liable to considerable local stress, such as is very liable to occur at +connections, so that the deflection is, whilst new, greater than after +many years’ use, by which time such parts may develop a definite “set,” +and contribute in a less degree, or not at all, to the total elastic +deformation. + +It is also possible, as already suggested, that repeated high stress may +reduce the ratio of strain to stress, the material gradually becoming +more rigid, the modulus of elasticity being, in fact, increased. + +In girders of ordinary construction, the major part of the deflection is +due to the booms, the remainder to the web; the latter is for plate +girders a small amount only, and is commonly neglected, but for open web +constructions it may be quite appreciable. For any given type of web +arrangement the deflection due to the web will, for all depths, remain a +constant quantity for the same span and unit stress; and though a +moderate fraction of the whole deflection for a shallow girder, it may +be a very considerable part for a girder of great depth, in which that +part due to the booms is, of course, smaller, since the deflection due +to these varies inversely as the girders’ depths. + +Deflection, being dependent upon the elasticity of the material, is of +necessity very largely influenced by the value of its modulus E, itself +liable to considerable variation, and is increased in a small degree by +the yield of joints and rivets, which effect, apart from the initial +“set” of the girders, appears to be negligible. The stiffness of members +in resisting angular distortion at connections must also, for open-web +riveted structures, affect the result, making it somewhat less, and, +finally, section excess at joints and gusset attachments has an +influence in modifying deflection as compared with that due to the +normal gross sections simply. + +From these considerations it is apparent that any simple deflection +formula must be largely empiric in its nature. For plate girders of +uniform depth and flange stress, the writer has found the following to +give good results:-- + + S^2 + ----- × _f_ = deflection in inches. + D × C + +The span S and depth D are, as a matter of convenience, taken in feet; +the constant C is for wrought iron 3500, and for mild steel 4000; _f_ is +the mean of the extreme tensile and compressive stresses of the booms, +in tons per square inch, estimated upon the gross sections. + +This, though satisfactory for plate girders, is not so suited to girders +having open webs, in which the deflection will more nearly be + + (3S S^2 ) + (-- + -----) × _f_, + (C D × C) + +the constant C being 3900 and 4450 for iron and steel respectively. The +latter values of C correspond to normal values of the modulus of +elasticity of 11,700 and 13,350 tons for iron and for steel, it being +assumed that any slight rivet yield is off-set by any small section +excess--say, 5 per cent.; it may, however, happen that section excess is +greater than assumed, in which case some allowance may properly be made +for this by increasing C. + +To adapt the formulæ to girders other than those having parallel booms +and uniform stress, the results, as deduced above, may be multiplied by +constants given in column B of the Table given on page 93. + +The practice of adopting for E in deflection formulæ a quantity much +smaller than its nominal amount, with the object of allowing in riveted +girder work for the yield of rivets and of joints, can hardly now be +defended, whatever may have been a case at a time when workmanship was +much inferior, when there was no machine riveting, and joints were, +owing to the small weight of plates and bars, three times as numerous. + +The initial “set” of a girder consequent upon first loading is a +quantity quite distinct from deflection proper, and may be so small as +to be negligible, or read 10 per cent. of the true deflection, varying +with design and workmanship. + +No estimate of girder deflection can be even approximately true if there +is, at the level of the top or bottom flanges, a plated or otherwise +rigid floor system which is not taken into account, as this will have +the effect of very materially reducing the boom stress. To neglect this +influence, where it exists, must necessarily lead to disappointing +results, and it is quite practicable in many instances to include it in +the calculation. + +The influence of angular distortion between the various members has been +neglected. It may be pointed out, however, that the resistance +accompanying these movements in girders having riveted connections, +though unimportant as affecting deflection, is worth some consideration +in regard to secondary stress. For girders of similar type and unit +stress these angular variations will be the same in amount for any span, +but will generally be of less importance in large girders than in small, +because in large girders the ratio of the breadth of members to their +length is commonly less. + +When determining the probable deflection of any girder of exceptional +figure, it will be found convenient to make a strain diagram--an old +device, in which the actual alterations of length being ascertained for +all members, the girder is carefully set out to a suitable scale, with +the lengths of members increased or reduced by the actual estimated +amounts. The distorted figure resulting will then give the probable +deflection. The value of E for this purpose should never be taken at +less than the normal amount, and may for a considerable excess of metal +in joints and gussets be made as much as 10 per cent. greater, this +being a convenient means of making the necessary correction. + +The effect of loads quickly applied may here be considered in connection +with elastic deformations of girders of the same span, but different +depths. If these be designed for similar loads and unit stresses, the +deflections due to webs and booms of the girders compared will bear the +same relation, each to each, as do the weights, whether in both cases +the loads be inert or quickly applied, from which it follows that the +mechanical “work” done by the loads in falling through the deflection +heights is, neglecting inertia, always in proportion to the girderwork +weights, and is a similar amount per ton, which as the total length of +members remains substantially unaltered, corresponds to a similar amount +of work per unit of section, or similar stress, irrespective of the +depth of the girders. + +But for a “drop” load, as when there is some obstruction upon a railway +bridge, there will be in addition a further amount of work to be +absorbed, which is to be considered the same whatever the girder’s +depth, and will for deep girders be a larger amount per ton of +girderwork than in those that are shallow; this, taking effect on +members of the same aggregate length, but lighter, will develop a higher +stress than in girders of lesser depth, more particularly in the booms. + +The influence of the girder’s inertia in modifying drop-load effects +will also be less marked in deep--i.e., light--girders than in girders +shallow and heavy. + +It is, notwithstanding all this, desirable that the depth of main +girders should be liberal for economy’s sake, and also that of floor +beams, for reasons already dealt with; the probability of the drop load +is somewhat remote, and, though possible, would simply induce, if it +occurred, an increment of stress rather more important in deep girders, +making it specially desirable in these to give particular attention to +the detailing of any connections liable to suffer from impact effects. + +It should be remarked that for short and very flexible beams, generally +outside the limits of practice, there may also be, under quickly moving +loads, a material increase of stress due to the centrifugal effort of +the load on running round the deflection curve, and in rising upon the +steep part of the curve beyond the girder’s centre. Where advisable, +these effects may be modified by cambering the rail. + +For pin bridges in which there may be spring in the pins, excess stress +in some eye-bars due to inequalities of length, and a want of that +rigidity peculiar to riveted structures, the deflection will be greater +than above indicated for girders of the ordinary English type. + +The method in common use for measuring the deflections of girders but a +moderate distance above the ground by means of sliding-rods, though +crude, gives, with care, results sufficiently accurate for most +practical purposes; but some points necessary to remember may be +mentioned with propriety. The lower rod should rest firmly upon +something solid, say a stone, well bedded and free from any tendency to +rock; the upper end should bear against some part of the girder above, +presenting a hard surface, free from dirt or scale, and as the running +load approaches the bridge it should be ascertained that there is no +slack, that the rods bear hard at the top and bottom. The upper end +having been depressed, care is to be exercised to make sure of the +reading before the rods alter their relation to each other. These +precautions are so self-evident that an apology is almost necessary for +mentioning them. + +To ascertain deflections with a single pair of rods is only allowable +when the girders rest firmly on their bearings; if felt has been placed +under the girder ends, or if the bedstones are insecure or rocking, it +is necessary to use three pairs of rods, one pair at the middle and a +pair at each end, in which case the mean of the two end readings must be +deducted from the reading of that at the centre to get the desired +result. + +In the case of a number of spans in series, each resting upon sill +girders common to two sets of bearings, this method also gives results +of indifferent reliability, as the depression of each end may be greater +as the travelling load comes upon and leaves the span than when it is +precisely over the middle, and it is in general out of the question to +secure by this mode simultaneous readings for a particular position of +the running load, which are what is required. + +The author suggests, as a means of ascertaining deflections free from +these objections, that it should be done by first measuring the slope at +one end, and from this deducing the deflection at the centre. + +This is to be accomplished by means of a little instrument, consisting +of a telescope with cross-hair sights, and fitted with a reflecting +prism at the eye-piece capable of being turned round, so that the +observer has a wide choice as to the position he assumes with reference +to the instrument, and may look either directly through it, or at right +angles to the axis of the telescope. This is clamped at one end of the +girder over the bearing, at the other end a scale is secured, to which +the telescope is directed, the cross hair being made to sight on the +zero of the scale, or the reading noted. For a girder supposed to +deflect to uniform curvature (say, with uniform depth and uniform +stress, the ordinary case) the reading observed will be four times the +deflection; every 1/10 inch actual reading on the scale will correspond +to 1/40 inch of girder deflection. + +Apart from the deflection, this method gives a ready means of observing +the end slope, a quantity of equal value for purposes of comparison. As +with girders of similar proportions, and similarly stressed, the +deflection will at all spans be the same fraction of the span; so should +the end slope be a constant quantity under similar conditions, the +diagram, Fig. 54, will make the principle quite clear. + +[Illustration: FIGS. 54 to 57.] + +Strictly the character of the deflection curve is slightly modified by +that part of the deflection due to the web; so that the depression at +the centre would, in the case assumed above, be somewhat more than +one-fourth part of the end reading, and generally will be a larger +fraction of the reading than that deduced from a consideration of flange +stress simply. In Figs. 55 to 57, which are intended to explain this, +it will be noticed that deflection due to the web is shown +straight-lined from the bearings to the centre of the girder; this is +strictly true only for a girder correctly designed for an immovable +distributed load; but as there should be for girders intended for a +travelling load, some excess in web members near the centre under the +condition of uniform loading, the point of the figure should be rounded +off to be in agreement with this case, though it is left as shown in the +diagram for the sake of simplicity. + +Suitable constants, including the corrections necessary, are given in +column A of the table annexed for a few typical cases, and by these +constants the actual readings should be multiplied to find the +deflection. The constants have been worked out for depths of one-tenth +the span; for greater depths they should be slightly more, and for +smaller depths somewhat less, but they may be used between the limits of +one-sixth and one-fourteenth, with a maximum error hardly exceeding 5 +per cent., and generally much less. + +The figures in column B relate to the formulæ previously stated, and +apply equally well to all depths. + +TABLES OF MULTIPLIERS FOR DEFLECTION. + + _Uniform Stress_: A. B. + Girders of uniform depth, varying flange section 0·27 1·00 + Hog-backed girders, ends half of centre depth, varying + flange section 0·24 1·08 + _Varying Stress_: + [1]Girders of uniform depth and flange section 0·32 0·87 + [1]Hog-backed girders (as above), but uniform flange + section 0·29 0·97 + [1]Bow-string girders of uniform flange section 0·16 1·30 + +[Footnote 1: For uniform loading.] + +It is apparent that, if preferred, the scale, instead of being in +inches, divided suitably, may, for each type of girder, be amplified to +the proper degree, so that the amount of the deflection may be read off +at once. + +This method of dealing with deflections is quite independent of the +character of the bearings, and is applicable to girders at any height +above ground or over water; but its use would hardly be practicable for +very small beams, or those in an awkward position, or near which it +would be impossible to remain with a running load upon the bridge. + +There is a possible source of error in the use of the instrument, most +likely to occur with triangulated girders, with which, if the instrument +is placed at the top of an end post, the reading observed may be the +joint effect of deflection and of local flexure of the members meeting +near the telescope. This may be tested, and, if necessary, allowed for, +by first sighting upon a scale at the next apex, and observing the +effect of the moving load. Again, as girders sometimes cant towards the +running load, if the instrument is placed on one edge of a girder, and +the cantings of the two ends are dissimilar, a false reading will +result, which may be amended by ascertaining the amount of cant at each +end, and correcting for the effect of the difference between the cants +upon the observation. Only in exceptional cases is it likely that either +of these considerations would need attention. + +The author has secured with this instrument very promising results, +notwithstanding that under a running load there is a slight haziness of +the scale as seen through the telescope, due to “dither,” largely the +result of imperfections which may be remedied. + +Deflections may sometimes be conveniently taken, by a quick-eyed +observer, with a good surveyor’s level and a specially-divided staff +held at the centre of the girder. The divisions preferred by the author +for this purpose are 1/10 inch, plainly marked, which may be seen at 50 +feet distance with sufficient clearness to make possible readings by +estimation between the divisions to, say, 1/50 inch. But it is clearly +desirable not to rely upon a single observation only, where all the +evidence is gone so soon as the sight has been taken. + +In rail-bearers, or other short girders, it may not be practicable to +adopt such methods, either on account of an inability to find a suitable +place for the instrument, or to read with any telescope with sufficient +promptitude as the load passes rapidly over. The use of rods may also be +out of the question, as the errors attending their manipulation may be +serious where but a small movement has to be noted, this being +complicated in some instances by the bearings being insecure, and +working to an extent which obscures the measurement sought. In such +cases it is preferable to use a stiff slat lying along the girder, which +bears, through short blocks over the girder bearings, upon the flanges; +the deflection is then read by direct measurement of the girder’s +depression at the centre, relative to the slat. + +The author is, unfortunately, not able to give any precise information +on the effect of running-load as against a load that is stationary in +connection with girder deflections. It is by no means easy in ordinary +work upon a railway to secure facilities for making such comparative +tests. It may, however, be confidently stated, as a result of such +observations as he has made, that the deflection due to a load coming +rapidly upon a bridge is, as to the main girders of, say, a 50 feet +span, but little greater than that due to the same load stationary; it +may be, perhaps, 5 to 10 per cent. more. + +It is evident that to determine the precise difference where the +quantity to be measured is so small needs apparatus of a more delicate +character than that in common use, and the control of an engine, or +engines, for the purpose of making the special tests, conditions which +on a busy line can only be secured by special arrangements previously +made. + + + + +CHAPTER IX. + +DECAY AND PAINTING. + + +The author has collected particulars as to the amount and rate of +rusting in metallic structures which are of some interest. In all such +instances it is very necessary to note the conditions which have +obtained during the process of wasting, as without this, misleading +conclusions may be drawn. The information given relates in all cases to +wrought iron, unless otherwise stated. + +A plate-girder bridge, having girders under rails, was found to be badly +rusted. The atmospheric conditions were unusually trying, the air being +damp and impregnated with acid fumes from adjacent steel works. That the +wasting was largely due to this latter cause was indicated by the fact +that the girders nearest to the steel works suffered more than those +farther removed and partly sheltered from the corrosive influence. + +The webs were in places eaten right through, having lost a mean amount +of about 1/8 inch full on each surface in twenty-eight years. Painting +had not been well attended to. + +In a similar bridge, not a great distance from this, but sufficiently +far away to modify the conditions for the better, considerable wasting +was also observed, but more particularly where the girders had been +built into masonry, which, loosening with the constant movement of the +girder-ends, had allowed moisture to collect, and rust to develop, +without the chance of repainting these surfaces. The amount of waste at +the places indicated was, as in the last case, about 1/8 inch on each +face, and in the same time, other parts of the girders having suffered +less. + +[Illustration: FIG. 58.] + +A third plate-girder bridge, with outer main girders, cross-girders, and +plated floor, carrying a road over a railway and sidings, and which was +known to have been neglected in the matter of painting, was very badly +rusted, both as to the cross-girders and floor-plates. The atmosphere +was somewhat damp; the chief cause of deterioration was, however, the +smoke and steam from locomotives, which frequently stood for some time, +during shunting operations, directly under the bridge. The webs of the +cross-girders, which were originally 1/4 inch thick, had rusted into +occasional holes during fourteen years--i.e. 1/8 inch from each surface +in that time. When removed a little later the wasting was so complete +that it was possible to knock out with a light hammer the remains of the +web between flanges and stiffeners, so as to leave an open frame only. +One of the cross-girders was so treated by the men engaged upon the +work, when it presented the appearance shown in Fig. 58. + +In another case--that of a bridge with lattice girders under rails--the +ends were built into masonry, which had, of course, loosened, with the +usual result. The air of the locality was certainly pure, but somewhat +damp. The general condition of the ironwork was good, but end-bars of +the diagonal bracing, where they had been closed in, had lost 1/8 inch +on each surface in thirty-three years. The top flanges immediately under +the timber floor were in a very fair state, which is of some interest +when it is considered that these were made of steel of the same kind as +that already noticed as being used in the construction of small girders +(see Fig. 46, _ante_), described in the chapter upon “High Stress,” both +cases dating from the year 1861. The painting upon the lattice-girder +bridge had been pretty well attended to; but in the case of the small +steel girders it had been greatly--perhaps altogether--neglected; this, +coupled with adverse atmospheric conditions, had produced the result +that the rate of rusting had for the small girders been much greater +than that of the steel top flange referred to, being fully 1/8 inch on +each surface, as against a negligible amount under the more favourable +circumstances. + +Girder-work over sea-water, as in piers, seems to rust at a sensibly +greater rate than inland work under average conditions; but it is hardly +practicable to make any strict comparison, as in either case the rate of +oxidation is so much affected--even controlled--by the care bestowed +upon the structures. This general conclusion is based upon the results +of examination of wrought-iron girder-work over sea-water of ages +varying from fourteen to forty-four years. It should be remarked, +however, that in one case steel girders but five years old, and which +were frequently wetted with sea-spray, were found to be wasting rather +badly--the paint refusing to keep upon the surface. + +It may be concluded from the above instances, and from others which have +come under notice, that wrought-iron work, if not properly cared for in +respect to painting, or under conditions otherwise bad, may be expected +to rust at a rate which corresponds to the loss of 1/8 inch on each +surface in from fifteen to thirty years; but with proper care as to +painting, and exclusive of exceptionally bad conditions, it does not +appear to waste at any measurable rate. In some instances, upon scraping +the paint from girders which had been in use for thirty years, the +author has found, beneath the original red lead, the metallic surface +bright and clean, showing no trace of rust. + +Of ordinary steelwork the same cannot be said, the common experience +being that mild steel is very liable to be attacked by rust. With +passable care in the bridge-yard during manufacture, such that with +wrought iron no after-trouble would be noticeable, steel is very liable +to show, within a year of being built up, numerous little blisters on +the painted surface; any one of these being broken away discloses a +small rust-pit. This is more often seen on the flange surfaces +(horizontal) than on web surfaces (vertical), but it is probable the +position has little to do with the matter, and that it is rather due to +the fact that rust has been earlier started on the flange-plates, upon +being put through the drilling-machines and inundated with slurry, which +occurs only to a more limited extent with webs having fewer holes. The +heads of steel rivets do not show this tendency to “pit,” or to early +development of rust. The riveting is about the last operation in making +a girder, each rivet being freed of all rust by heating, and quickly +coming under the protection of oil or paint. It may happen in this way +that the heads of rivets on a girder may be exposed without protection +for as many hours only as the rest of the work for weeks, which fully +accounts for the difference in behaviour. + +The essential point to be observed in all steelwork is to prevent, if +possible, the first development of rust, for once begun it is much more +difficult to arrest than in iron; for this reason, oiling of all +material for a steel bridge, at a very early stage of its existence, +cannot be too strongly insisted upon. This practice, however, makes the +work so objectionable, and even dangerous when being lifted--because of +the liability to slip--to the men engaged upon it, that it is commonly +very difficult to ensure it being done sufficiently soon to satisfy a +careful inspector. If the work is carried out under cover, the +requirement is less urgent. Strictly, all material should be oiled so +soon as rolled, but the author does not remember to have seen this done +at any of the mills he has visited, though it is common enough to find +it specified. + +Ironwork does not need the extreme care which should be bestowed upon +steelwork, but it is desirable that it should be painted as soon as +possible, the surfaces being first thoroughly cleaned. + +There is, probably, for painting girder work nothing to beat good red +lead as a protective coating; but there is considerable difficulty in +getting it reasonably pure, without which quality its utility will be +greatly reduced. The question of purity will, however, be found to be +largely a question of price. It may be stated broadly that, whether for +steel or for iron, the first protective covering is, perhaps, the most +important of any it will ever receive. + +In repainting old work, care should be taken to remove all traces of +rust previous to laying on the new coat. It is not an altogether +uncommon practice to repaint old structures by dealing only with the +parts readily accessible, which, being less liable to rust, probably but +little need it; leaving those parts which are difficult of access, and +where rust is developing, untouched; treating the whole business as a +matter of appearance simply. This, it need hardly be said, is +indefensible. It is better rather to neglect the surfaces freely exposed +and ventilated, and devote the whole care upon those other parts, +confined and difficult to get at; taking the trouble necessary to remove +ballast, timber, or whatever may obstruct the operation, in order that +the bad places may be thoroughly scraped, and then painted. Those parts +which most need attention may cost, perhaps, to reach--and deal with +when exposed--ten times as much per yard of surface as the rest of the +superfices, which needs little, and is always accessible; but the cost +should not deter the proper carrying out of the work, as it will prove +the very worst sort of economy to deal with painting in a perfunctory +manner. + +It should be noted that girder work, whether of wrought or cast iron, +when embedded in lime or cement concrete, or mortar, generally proves to +be very well preserved, provided that close contact has obtained. +Cast-iron girders, when carrying jack arches resting upon the bottom +flanges, are found after long use to be in remarkably good order, when +finally taken out, having, indeed, the surface appearance of new +girders. Much the same remarks apply to girders of wrought iron carrying +jack arches, where protected by the brickwork; provided that the girders +are sufficiently stiff to minimise deflection, and allow the masonry or +brickwork to adhere to the surfaces. + +Such girders are in a very different condition to those previously +referred to, in which the ends of the girders, carrying a light floor +structure, are built into masonry where the deflection slope is +greatest; though, apart from the few cases where adherence can be relied +upon, building-in is an undesirable practice, and has the disadvantage +that after-examination is only possible by removing portions of the +masonry, which it is evident would very seldom be resorted to. + +Cast iron has ordinarily--unlike wrought iron or steel--great capacity +for resisting rust, and will, after many years of absolute neglect, +appear but little the worse; an advantage which is the more pronounced +when considered relatively to the greater thickness of the thinnest +parts in cast-iron girders, the percentage of waste being +proportionately lessened. + +Cast iron does, however, behave somewhat badly in sea-water, the metal +sometimes losing its original character, and becoming in time quite +soft; though, if not worn away, as by the attrition of shingle, +maintaining its original bulk. + +Of some forty-five cast-iron piles belonging to various structures, +examined whilst engaged upon sea-pier work for Mr. St. George-Moore, +though the author found somewhat diverse results, in no case did there +appear to be any general softening of the whole thickness, but a +distinct change for some definite distance inwards, generally to be +decided without difficulty, beyond which the metal appeared to retain +its original character. In all cases any material depth of softening was +found close to the ground, this depth rapidly decreasing higher up, +till, at a height of 5 feet, but little if any softening could be +detected. At 2 feet above ground the softening was frequently but +one-quarter of that at ground level. There was, too, often a +considerable difference in the behaviour of different piles in the same +structure under similar conditions; one pile being found to have only +one-fourth part of the softening noticed in others, or possibly none at +all. For six different structures the amount of softening near ground +level, of about twenty-five piles examined, was as given in the table on +the next page. + +The greatest depth of softening found (see No. 2) was 9/16 inch, 1 foot +above ground, in a pile thirty-six years old. The decayed material when +removed was of a soft, greasy consistency, perfectly black, which a few +hours later was found to have changed to a dry yellow powder, by the +rapid absorption, it may be supposed, of atmospheric oxygen. It is +apparent, therefore, from this example that deterioration may proceed to +a considerable depth; but it should be observed that other piles of the +set showed softening at ground level of 1/8 inch only. + +SOFTENING OF CAST-IRON PILES IN SEA-WATER. + + ---+--------+----------+-----------+----------+---------+--------- + No.| Age. | Maximum | Maximum |Mean Rate | Quality |Materials + | |Softening.| Rate of | of |of Metal.|Entered + | | |Softening. |Softening.| |by Piles. + ---+--------+----------+-----------+----------+---------+--------- + 1 |17 years|5/16 in. |1/8 in. in |1/8 in. in|Soft |Extremely + | | |7 years |15 years | |soft + | | | | | |sandstone. + 2 |36 years|9/16 „ |1/8 in. in |No result | „ |Rubble + | | |8-1/2 years| | |mound. + 3 |32 years|3/8 „ |1/8 in. in |1/8 in. in|Moderate-|Fine + | | |11 years |15 years |ly hard |sand. + 4 |38 years|1/10 „ |1/8 in. in |1/8 in. in|Hard |Extremely + | | |47 years |140 years | |hard rock. + 5 |17 years|Small |Negligible | |(?) |Sand and + | | | | | |Shingle. + 6 |14 years|Negligible|Ditto | |(?) |Sand. + ---+--------+----------+-----------+----------+---------+---------- + +The least rate of softening noticed, apart from those structures of a +more recent date, in two of which it was very slight, occurred in a +pier thirty-eight years old (No. 4), where, of three piles tested, two +were quite hard, and the third softened 1/10 inch only. + +Whatever may be the precise cause of the change, it does not appear to +be affected by the period or percentage of immersion during the rise and +fall of tides. + +[Illustration: FIG. 59.] + +This will be clear from the diagram, Fig. 59, which refers to four piles +(No. 3 of table), all of the same age, in the same structure. On each +pile the depth of softening is given at points in strict relation to +each other, and to the tidal range. The percentages of immersion for the +various heights are also given, from a study of which it will be +apparent that these have no relation to the amount of softening; this, +indeed, is always greatest near the ground, at whatever actual height it +may be. For instance, pile A was at ground-level softened 1/4 inch, +that point being 60 per cent. of its life under water; but on pile B, at +a point 74 per cent. of the time submerged, and 4 feet above a lower +ground-level, no softening was apparent; further, at ground-level of +this pile, the percentage being there 87, the softening was no greater +than at ground-level at pile A. + +It is probable that while the percentage of submersion in moving water +hardly appears to affect the result, yet prolonged contact with wet +sand, sea-weed, or clinging shell-fish may do so. This seems to suggest +that the process of change, as between the sea-water and the iron, is +slow, and to be effective must be continuous; so that it is only found +to any considerable extent where the water in contact with the surface +is still. In the two worst cases, Nos. 1 and 2 of the table, at points 1 +foot and 6 inches above ground-level, the surface was in one pile +shrouded in a thick mantle of heavy sea-weed, and in the other covered +by molluscs; in both instances the surfaces being thus kept moist and +undisturbed. The piles of the fourth case were in hard rock, were clean, +and, where accessible, always either in moving water or quite dry. + +However this may be, the power to resist softening certainly appears to +vary largely with the quality of the iron. The piles, referred to above, +in which deterioration proceeded at the most rapid rate were certainly +of a soft metal, the first being markedly so. On the other hand, certain +piles (No. 4) of hard, close-grained iron suffered very little. + +It may be mentioned with respect to the last named, as a matter of +interest, that the caps of the lower lengths (just above ground-level) +had been cast with short pieces of wrought iron projecting--possibly for +lifting purposes--which during thirty-eight years had altered in +character to something very like softened cast iron, but laminated, and +harder. Of about 1-1/4 inch original thickness, only 3/16 inch remained +having the semblance of wrought iron. The percentage of submersion was +about 60. + +A number of piles, not included in the table, varying from fifteen to +forty-four years old, and of the same structure to which set No. 2 +belonged, were all found to be hard, with the exception of one showing +3/16 inch of softening. These are omitted, because the mud surrounding +them was at the time of examination unusually high, so that the more +normal ground-level could not be reached, at which points testing might +have disclosed different results. It is probable that for any piles +standing in soft material examination below the surface would reveal +more pronounced softening than where occasionally exposed. + +To meet the effects of sea-water on cast-iron piles, and for other +reasons, it is a common and good practice to make the lower lengths of +greater thickness--say, 3/8 inch more--than that sufficient for the +upper. Occasionally, also, the bottom lengths are filled with concrete, +which no doubt adds to the length of time during which they may be +relied upon. + + + + +CHAPTER X. + +EXAMINATION, REPAIR, AND STRENGTHENING OF RIVETED BRIDGES. + + +In the preceding chapters defects of various kinds to which riveted +bridgework is liable have been more particularly dealt with; it is now +proposed to consider the examination of such structures, following this +by a reference to methods of repair and strengthening, leaving the +treatment of other classes of bridgework to be developed under their +proper headings, though some of the remarks immediately following will +apply to all. + +The exhaustive survey of a bridge is only to be made after considerable +experience in the work, but it may be stated that in looking for defects +it is well to seek where they are least expected, till, with practice, +one knows better where to direct attention. When examining with a view +to pronouncing an opinion upon the fitness of the structure to remain in +place, if in any real doubt, it is wise to give a casting vote against +it; and finally it may be said that upon taking down a bridge condemned +for any one or more defects, it should be examined for worse. This may +seem to be somewhat pessimistic, but is based upon the teachings of +experience. + +Preliminary examination of a bridge may reveal such faults or weaknesses +as at once to ensure its condemnation; but if this is not the case, and +there is a reasonable probability that the structure may be given a +fresh lease of life, it will, for the purpose of estimating the +strength, or for possible repairs, commonly be desirable to secure +precise particulars of the existing structure independently of any +drawings that may be in existence, and which will very probably be +incorrect, the finished work, if old, seldom agreeing with the contract +drawings. A final decision may in this case be deferred till after the +measuring up has been completed, the condition of the structure becoming +more familiar in the process. + +It is desirable first to ascertain whether the bridge remains in good +form, whether the camber of girders appears to be what might be +expected, or agreeable with existing records, though much reliance must +not be placed upon figured cambers, it being quite common for girders to +leave the bridge yards with the camber something other than that +intended. The deflections under live load will also be observed, and +compared with the calculated result, or checked by judgment. The +calculations upon which strength and deflections are based will, of +course, refer to the actual sections, which are sometimes a little +difficult to ascertain if there has been irregular rusting. In +continuous girders also, levels having been taken, allowance should be +made for effects of settlement, if any; and with arches evidence of +movement of the piers or abutments sought for, with the like object. It +is seldom that the main flanges of girders show signs of weakness, +unless from flexure in the case of long and narrow top members, +insufficiently stiffened; but there may be want of truth from other +causes already dealt with. In plate girders the webs should be most +carefully scanned for possible cracks, particularly where cross-girders +are connected, and along the upper edges of bottom flange angles, if the +floor rest upon the flange. All riveted connections, of course, need +close attention, both for straining effects, where there is a liability +to wracking, and to detect loose rivets. Loose rivets and want of +tightness in other parts of the work may frequently be detected at +sight by a reddish bloom which appears on the neighbouring surfaces, +caused by rust working out and spreading under the effects of weather; +it may be seen round rivet-heads or along the edges of angle-bars, or +other parts where there is movement. Loose rivets, though generally to +be detected also by the hammer, may perhaps in the case of thin-webbed +cross-girders be working in the web-thickness only, possibly to a +considerable extent. This, if not otherwise evident, may sometimes be +detected by simultaneous deflection tests--with rods--at the top and +bottom flanges of a girder, at the same distance from the bearings. Any +difference in the readings may indicate loose web-rivets, or possibly a +tear in the web running parallel to the flange angles. + +Bracings between girders are very apt to display a rich harvest of +working rivets. Cross-girders and longitudinals also may have loose +rivets at their connections, and be very badly wasted, with quite +possibly cracks in the webs, or other defects already enlarged upon. + +The condition of the road upon the bridge will frequently be an +indication of the state of the floor which carries it; or the existence +of rail-joints which are working badly may very properly lead to a +critical examination of the girder-work immediately below, as this is a +fruitful source of damage in light constructions. Floor-plates, where +these exist, should be scanned for leakages, drainage nozzles, and +guttering, to see that they are free, the attachments of the latter +being often loose and unsatisfactory. + +Trough floors may be expected to show loose rivets near the ends, with a +probability of excessive leakage where they abut against the webs of +supporting girders. + +Floor plates resting upon abutments or piers, being very liable to +serious decay, require attention, and girder-work entering masonry +should receive close scrutiny, any obstruction to a sufficient +examination being removed so far as is judged sufficient for the +purpose. The structure should, of course, be closely watched during the +passage of live load for any signs of abnormal movement, excessive +vibration, or lurching. + +In addition to seeking for these various defects, or others which have +been referred to in these pages at length, it will be well always to be +alive to the possibility of faults to be seen for the first time, or of +which the author has furnished no instance. + +Having formed a reliable opinion as to the state of the bridge, this, if +satisfactory, may leave to be determined only the question of strength +relative to the loads carried. It is apparent that stress limits +suitable for a new structure, which has all its life before it, of +purpose moderate to cover possible deteriorations, the growth of loads, +and other adverse influences, may to avoid immediate reconstruction, +reasonably be permitted of a higher value for a further term of years in +the case of a structure which it is known has for a considerable period +behaved well, and remains in good condition. What this higher value may +be will be greatly influenced by the circumstances of each case, and, +being largely a matter of judgment, may be expected to vary with +different engineers. Experience shows, however, that the nominal unit +stress in an old bridge may be a very considerable amount in excess of +that allowed for new work, without, of necessity, showing any ill +effects; and the author is of opinion that for old bridges in good +condition it is quite prudent to allow an excess of 33 per cent. beyond +that permissible for a new design. If the structure is too weak to +satisfy this modified condition, it may be possible to bring it within +the stress limit by a reduction of ballast or other removable dead +weight. If this expedient does not promise to be satisfactory, or the +bridge shows actual signs of weakness, or palpable defects, it will be +necessary to deal with the question of repair, strengthening, or +reconstruction. + +The repair of built up bridgework resolves itself largely into a matter +of replacing loose rivets by cutting these out, rhymering the holes, if +desirable, and again riveting. It will often be sufficient to do this +with no particular precautions as to bolting up temporarily; the rivets +having been loose, may very well be spared for a time. In re-riveting +cross-girder connections it may, however, be imperative to remove all +the rivets, bolting up securely as this is done, in order to make a +tight job, taking out each bolt in turn as required, and again filling +the holes; or it may be well in a bad case first to remove all loose +rivets, substituting good bolts, in order that work which has gone out +of shape owing to defective rivets may first be brought true. + +Cross-girder webs, cracked vertically or nearly so, are commonly +repaired with splice-plates on either side; but in doing this it is +undesirable to add plates of excessive thickness relative to the +web--probably poor--as by an abrupt change of web section it appears not +unlikely a fresh break may be favoured. + +[Illustration: FIG. 60.] + +[Illustration: FIG. 61.] + +[Illustration: FIG. 62.] + +[Illustration: FIG. 63.] + +Replacing wasted flange-plates, or adding new plates to those which +exist, is occasionally resorted to in the case of main girders, the +flanges of which are sufficiently accessible, but the operation is +difficult, takes some little time, and should only be attempted under +the constant supervision of a thoroughly capable man. When done, if the +girder has not been relieved of load by staging, the stress under full +load will be unequally distributed between the old and the new section, +the old always taking more by the amount of the dead-load stress +previously carried. The method which the author has seen applied to +lattice girders of about 80 feet span, having good angle-bars in the +flanges, with a shallow vertical web for attachment of diagonals, +consisted in first cutting out the old flange rivets, and substituting +bolts well screwed up, till all the rivets necessary had been removed. +The new plate length having been prepared, was, on a Sunday, during a +few hours’ cessation of traffic, marked off, the temporary bolts being +removed for the purpose, and then replaced. After the plate had been +drilled, on a later Sunday, it was finally put into position, bolted up, +and riveted at leisure; cover-plates make additional trouble, but are +dealt with on the same principle. The method as shown in Fig. 60 is, +however, barely practicable for so many plates. It is preferable, if it +is proposed to add section, to do this with as little interference as +possible with existing rivets of importance. This may be accomplished, +if the existing plates are not too wasted at their edges, by riveting on +new strips or angle-bars (see Figs. 61 to 63). Occasionally the strength +of a girder is increased by the addition to the top or bottom boom of +material in such a form as sensibly to increase the depth, and thus, +while adding increased section to one boom, to reduce the stress in +each, though to dissimilar amounts. By this device also the relief is +effective only as regards the live-load stress; under dead load only the +new material does no work, provided, of course, that no relief staging +was used during the alterations. For girders carrying any considerable +proportion of dead load the method is very inefficient, though for +others, in which the live load is relatively large, the result should be +more satisfactory. + +As this question of adding new section to old is of much importance in +dealing with repairs and strengthening operations, a few general remarks +upon the subject will be pertinent. The difficulty in such work commonly +is to cause the new to render any considerable assistance to the old in +those cases which occur in practice. If a bar be imagined under +longitudinal stress varying between 0 and a maximum, then, if the area +of the piece be increased at the time when it takes no stress, its +capacity for resisting the maximum amount will be increased, and for +added material of similar elasticity the unit stress proportionately +reduced. If, however, the load on the bar does not vary, the mere +addition of metal will not relieve the original section in any degree. +To take a third case, of the maximum being twice the minimum load, it +will be necessary, in order to lower the maximum unit stress by 25 per +cent., to double the original section of the bar if, as supposed, the +extra metal has been added to the piece when under the smaller load, so +that the new section is only effective in assisting to carry the +remainder of the load at such times as it may be imposed. The +relationship stands thus:-- + + Live load New area + ---------------- × -------------- = relief. + Live + dead load New + old area + +These statements will be true under the conditions named, within the +elastic limit of the material; but some advantage would be derived in +the second case, and a more marked benefit in the third, if the load +assumed to be a maximum were exceeded, or if the composite bar were +tested to destruction; as, however, these effects would be outside the +limiting conditions imposed, it must be a matter of judgment as to how +far this reserve of strength may be considered of value. + +If, instead of simply adding section to the bar, some part of the +constant load is put upon the new section by the manner of attachment, +the combination will, of course, be more effective. + +To apply these considerations and illustrate the way in which the two +methods of adding flange section work out when reduced to figures, the +case will be supposed of a girder 6 feet deep, carrying a load of which +one-third is dead and two-thirds live. To the flanges of this girder are +added plates equal to 50 per cent. of the original areas, in order to +reduce the stress of 7 tons per square inch to which the girder before +strengthening is liable, the depth remaining substantially unaltered. +With dead load only the original section would be stressed to 2·3 tons +per square inch, the new section being then unstressed. Under full load +the new and old material take 3·1 tons per square inch additional, +making the modified stress on the original section 5·4 tons per square +inch, as against 7 tons; or a reduction of 22 per cent. This compares +with 33 per cent., the relief due to 50 per cent. increase of flange +area under ordinary conditions of stress distribution. + +Let the second method of strengthening the girder now be considered, +using, for purposes of comparison, the same total amount of new material +to increase the girder depth by an addition to the top flange. This +section will be equal to the area of one flange, which, though it may +be applied in many different ways, giving a greater or a less increase +to the depth, would probably be used in some such manner as that shown +in Fig. 64, increasing the effective depth for live-load stress by +nearly 10 inches. + +[Illustration: FIG. 64.] + +The added material will, as in the previous case, leave the dead-load +stress unaltered, or 2·3 tons per square inch. The stress in the bottom +flange due to live load will, however, now be 4·1 tons per square inch, +making a total stress of 6·4 tons per square inch, against 7 tons--the +original stress. The reduction here is 8 per cent. only, as compared +with 12 per cent., the relief due, under ordinary conditions, to an +increase of effective depth from 6 feet to 6 feet 10 inches, and by the +use of additional material, equal, as before, to one-half of the total +flange areas before the alteration. + +The effect on the top flange need not be here gone into in detail, but +it may be said that, owing to the increase of gross section and of +depth, the ultimate stresses of both the new and old material are +greatly less than as given for the bottom flange. + +Girders strengthened by the first of these two methods would, it is +probable, if tested to destruction, give results more nearly in accord +with the actual percentage increase of flange section, plastic +deformation of the metal, before failure, tending to reduce the +differences of stress on the new and old material of the sections. + +[Illustration: FIGS. 65 and 66.] + +Web members of lattice girders may, if weak, sometimes be dealt with by +the introduction of supplementary bars, parallel to and between the old +members, or by the addition of strips or angles to the existing +diagonals. The treatment will be largely influenced by the nature of the +old detail, which may lend itself to some one arrangement much better +than to any other. + +End riveting of web members may, if it has become loose, be dealt with +by simply rhymering the holes a size larger, and re-riveting in the best +manner, if the stresses are not excessive; or it may be necessary to +devise some additional attachments by which new rivets are brought into +use (see Figs. 65 and 66). The effective relief due to supplementary +rivets will be influenced by similar considerations to those governing +increase of section. + +[Illustration: FIG. 67.] + +[Illustration: FIG. 68.] + +Old structures are very frequently deficient in bracing, which may, in +such cases, be advantageously introduced; or girders individually weak +may be rendered collectively efficient by suitable bracing. In +considering the advisability of this, however, the case should be viewed +with regard to the possible effects of such members, as already dealt +with in the chapter relating to these questions. There it has been +pointed out that bracing between a system of parallel girders may have +the effect, under live load, of increasing the stress on the outer +girders due to twisting of the structure as a whole, though the inner +girders will, except for full loading of the whole bridge, be advantaged +as to stress values, and in any event bettered by being held up to their +work. The effect upon the outer girders may be met by increasing their +strength, if this appears to be necessary. In all such alterations the +detail should be schemed with special care to ensure simplicity in +execution, smith’s work being rigorously avoided. A good arrangement for +supplementary bracing between plate-girders, which gives little trouble +in carrying out, is shown in Fig. 67; or where the stiffeners of such +girders are in line across the bridge, the detail given in Fig. 68 may +involve less expenditure. Difficulties may be experienced in riveting, +unless great care is taken in the positioning of rivets. Fitting-bolts +are only to be relied upon as such, if they really justify the name; +they are, though easy to specify, by no means easy to secure under the +conditions of practical work. Weak cross-girders may make +alterations--in some cases considerable--necessary, to rectify the +defect of strength. The removal of old girders to make room for new is +seldom resorted to, unless the existing detail renders this a simple +operation; but it is not unusual to introduce new girders between the +old in cases where there is no plated floor to make the work difficult. +By this method there is, of course, an increase of appreciable amount in +the dead load carried by the main girders, which would in many instances +be objectionable. With deep and heavy main girders, having plate webs, +cross-girders may be strengthened by improving the end connections by +suitable gussets, and attachment to good vertical stiffeners, the fixity +of the ends thus aimed at being assured by overhead struts or girders, +from one main girder to its fellow, at intervals apart well considered +with reference to the horizontal strength of the top flanges, the whole +thus making a closed frame, as shown in Fig. 69. The method appears +feasible, but it should be stated that the author has not known it to be +applied in its entirety as a means of strengthening an old floor. + +[Illustration: FIG. 69.] + +A simple and very common device consists in substituting for the +ordinary cross-sleeper road, where this exists, stout timber +longitudinals under the rails, which have, where the cross-girders do +not exceed 5 feet centres, a marked distributive effect, tending to +reduce the maximum load upon any individual girder. With a similar +object, trough girders containing longitudinal timbers are sometimes +adopted where the depth available is not enough to enable sufficiently +stiff timbers to be used alone. In either case the object sought is the +same--to modify the effect of the heavier wheel loads upon isolated +cross-girders. When the spacing is so close as 4 feet, the beneficial +result of this treatment is considerable, but at 8 feet centres it can +have but a moderate effect where timbers alone are used. + +Occasionally, for long cross-girders, a distributing girder is placed, +with the same intent, in the 6 feet way, its function being limited to +this use only if the depth and strength are sufficiently small to serve +this object alone, as distinct from the case in which it becomes a +carrying girder transferring load to the abutments. As a distributor +simply, the girder has to equalise the bending moments amongst the +cross-girders, to effect which it will be evident that these moments +having been ascertained for the several cross-girders previous to +alteration, for a position of the wheel loads such that the heaviest +comes upon a centre cross-girder, the mean of these moments will, when +compared with that for each girder, show the difference to be induced as +a result of introducing the distributor. These differences of moment +render necessary at the centre of the cross-girders reactions upwards or +downwards, as the case may be, of amounts competent to induce moments +below the inner rails equal to these differences. + +It is these reactions which must be provided by the distributing girder +at a moderate stress, and without flexure of such an amount as sensibly +to modify the reactions. The greatest section necessary at any one point +may then be adopted for the girder throughout. The result will commonly +work out to a moderate section, but there will be no harm in a little +excess in a case of this kind, the total cost being but little affected +by some small addition to the weight, where labour upon the site is so +considerable an item as in work of this description. The ends of the +distributing girder should be carried on to the abutments or piers to +ensure adequate relief of the end cross-girders. It will be found +desirable in arranging for distributing girders to ascertain at an early +stage, by boning or by levelling, the condition of the cross-girders as +to uniformity of heights, as this may affect the length most suitable +for separate sections. Between the underside of the distributor and the +cross-girder tops there will commonly be spaces of varying amounts, +which should be filled by packings to fit, rather than by pulling the +work together by force, introducing undesirable stresses of uncertain +amount. + +In the earlier remarks upon the strengthening of bridgework by the use +of new material, it has been assumed that the modulus of elasticity of +the new metal is similar to that of the old; it may, however, as in +cases where wrought-iron work is reinforced by additions in steel, be +necessary to take the difference of elastic properties into account, +with which object the new section should be multiplied by a quantity +(greater or less than unity) inversely proportional to the higher or +lower modulus of the new material, that is to say, by + + E of old material + ----------------- + E of new material + + + + +CHAPTER XI. + +STRENGTHENING OF RIVETED BRIDGES BY CENTRE GIRDERS. + + +The addition of distributing girders, described in the last chapter, as +a means of strengthening a bridge floor, while sufficient in many cases +so far as the cross-girders are concerned, does not in any appreciable +way assist the main girders. When for a two-line bridge, having outer +main girders only, this result also is desired, together with a more +complete relief of the floor structure, centre main girders may be used, +placed either above or below the cross-girders, on the centre line of +the bridge. + +There are two principal ways in which such a girder may be brought into +use; the easier, but generally less economical, is by making a simple +attachment to the cross-girders, the old girder work still taking the +whole dead load. By this method the new girder does no work but carry +itself till the live load comes upon the bridge, and must be made very +stiff to take any sensible portion of the running load; the second +method is to make the connection adjustable, so that a part of the floor +weights may be imposed upon the new girder as an initial load. In doing +this the old outer girders will rise slightly, being relieved of stress, +and the cross-girders also lifted at the middle, whilst the new girder +is depressed as the load is brought upon it. With some part of the live +load a very considerable proportion of the total may in this way be +carried by a centre girder of moderate section. The whole question, by +either method, turns upon deflections; and it is in determining the +relative movements of the girders that the problem chiefly lies. + +It is convenient first to determine the percentage of load relief to be +effected in the main girders, as to which it is to be observed that as +this relief (distributed) is induced by the upward reaction of the new +girder acting at the centre of the cross-girders, the stress relief of +these will, as a rule, greatly exceed that of the outside girders. For +the generality of cases, it may be taken that the relief suitable for +the outside girders will be satisfactory in its effects upon the +cross-girders, even though it is desired to reduce the stress in these +to a greater degree. + +If, however, it be thought desirable to check this, it may be done by +considering a cross-girder subject to its dead and live loads acting +downwards, and to reactions at the centre and ends. At the centre the +reaction will be the load of which the two main girders are relieved on +a length equal to the pitch of the cross-girders, or as here given:-- + + _c_ × _t_ × P = reaction at centre (1) + +_c_ being the percentage of relief; _t_ the total load per foot run of +the bridge; and P the pitch of cross-girders. The live loads carried by +the cross-girders are for this purpose taken at per foot run, as for the +main girders. With these data it will be easy to construct a diagram of +moments, making it evident whether the relief proposed for the main +girders will give a sufficient percentage of relief to the floor beams. + +Granting that this proportion has been decided, and dealing first with +the case in which the centre girder is simply attached to the +cross-girders, and takes no dead load other than its own weight, then +the live load carried by the outside girders, and previously borne +wholly by them, will be reduced by the amount it is intended to transfer +to the centre girder, and will become + + L{_l_} - (_c_ × L{_t_}) = live load on outer girders (2) + +L{_l_} being the total live load, and L{_t_} the total dead and live +load carried by the bridge. From this the deflection of the outer +girders corresponding to this modified live load may be derived. + +[Illustration: FIG. 70.] + +It is next necessary to ascertain the vertical movement, commonly a +depression, of the cross-girders at the centre relative to their ends, +when subject to the running load only, and supported at the middle and +ends, the centre reaction being obtained as before indicated (1). This +movement will be the difference (if any) between the deflection on the +whole span of the cross-girder due to the live load, and the upward +flexure of the girder due to the centre reaction, considered as separate +effects. Stress values having been estimated for the two conditions, +these results may readily be deduced by simple flexure formulæ, +observing that while the curve of moments due to live load sufficiently +approximates to that for a distributed load to justify, for this, the +use of a distributed load formula as given in the chapter “Deflections,” +the flexure due to the centre reaction will be but 0·80 of that which +corresponds to the same stress for distributed loading. Or, the curve +assumed by the girder under live load may be plotted by a method to be +later explained. + +The sum of the movements now determined--that is, the live-load +deflection of the outer girders, and depression, as is commonly the +case, of the cross-girders--will give the extreme depression (marked _m_ +in Fig. 70), from the dead-load condition of the middle cross-girders, +when supported to the extent desired by a centre girder whose +proportions are not yet known, but which, carrying the required +percentage of the total load, must, subject to a reservation presently +stated, deflect only this amount. The unit stress in the flanges of the +new girder, governed by this flexure, will for a plate girder be + + D × C × _m_ + ----------- = _f_, unit stress on gross section (3) + S^{2} + +D and S being, as before (see “Deflections”), the depth and span +respectively in feet, C a constant, _m_ the deflection in inches, and +_f_ the stress per square inch on the gross section of flange. + +The gross area A, of the flange, is given by + + S × _c_ × L{_t_} + ---------------- = gross area of flange (4) + 8 × D × _f_ + +_c_ × L{_t_}, being, as in (2), the load transferred to and carried by +the centre girder. + +The actual stress in the flanges will, of course, be greater by an +amount due to the girder’s own weight; but this does not affect the +question of relief. For any ordinary case the stress per square inch +will be low; but it will manifestly be useless to assume a greater +stress with a view to economy, as the effect of reducing the section +will simply be to make the girder too flexible, thus causing it to be +less effective than primarily intended. If, as is seldom the case, there +is freedom as to the depth of girder permissible, it is evident the unit +stress may be made a condition, and the depth deduced by a suitable +modification of formula (3); the relief desired being in this way +equally well assured. Indeed, in the rare instances in which any depth +may be adopted, this method is--contrary to the general rule--distinctly +economical, particularly if the girder may be placed below the +cross-girders, which simply rest upon it, without elaborate attachments. + +[Illustration: FIG. 71.] + +Considering now the second method of applying centre girders by which +the new girder is made initially to carry part of the dead load, by +adjustment, it will at once be recognised as a more complex matter. The +measure of relief by which the old girderwork shall benefit need not be +affected by the method of applying the centre girder, and may be decided +on the principles already considered. The outer girders carrying a +reduced load, when the bridge is fully loaded, and the cross-girders +being in part supported at their centres in the manner already +described, will give a resulting depression _m_ (see Fig. 71) of the +centre cross-girders, below the original dead-load position, of a +similar amount determined in the same way. This extreme depression +determines also the lowest position of the new centre girder, which may +be designed to carry the required percentage of the total bridge loads +with the maximum stress and depth, as conditions, leaving the initial +dead load and necessary adjustments to be ascertained. This is the +common case and will be here dealt with, it being assumed to avoid +ambiguity in description that the new girder lies above the +cross-girders. + +The centre girder of fixed depth being then required to carry a definite +load at a definite flange stress, will deflect a definite amount at this +stress. If this deflection equalled the extreme depression _m_ of the +old girder work, no adjustment would be necessary, the centre girder +then carrying no initial dead load, as by the first method; but for +centre girders designed for economical flange stress the deflection will +in ordinary cases greatly exceed this, the depth generally being small, +and in order to ensure that the new girder shall do its full work, some +dead load must be put upon it. In the act of adjustment the +cross-girders must be lifted and the centre girder depressed, till the +joint movement equals the excess _s_ of the centre girder deflection +over _m_, when the new girder will carry the proper amount of initial +load, and upon further deflection under live load give the full measure +of relief. The amount of “lift” or upward flexure of the old girder +work, and the depression or “drop” of the new girder, during adjustment, +will depend upon relative stiffness, and may be ascertained as +follows:-- + +For unit reactions at the centre of the cross-girders the upward flexure +of these may be ascertained, as also the upward flexure of the two outer +girders when subject to forces of the same total amount (one-half to +each) applied at the cross-girder ends. The sum of these movements will +give the total lift of the centre cross-girders, when all are subject to +unit lifting forces; similarly, the depression of the centre girder for +unit loads applied at the cross-girders may be determined. There will +then be known the movements upwards and downwards of the old and new +work when being drawn together by unit forces applied as stated. + +If + + _l_ = lift due to unit loads, + _l{t}_ = total lift due to adjustment, + _d_ = drop due to unit loads, + _d{t}_ = total drop due to adjustment, + _s_ = deflection excess = gross adjustment, + +there will then be + + _d_ + --------- × _s_ = _d{t}_, + _l_ + _d_ + +total drop of centre girder under adjustment, + + _l_ + --------- × _s_ = _l{t}_, + _l_ + _d_ + +total lift of centre cross girders under adjustment, + + _d{t}_ + ------ × unit load = + _d_ + +initial load put upon centre girder at each cross-girder. + +The rise of the two outer girders for upward forces together equal to +those depressing the centre girder may readily be deduced. + +[Illustration: FIG. 72.] + +[Illustration: FIG. 73.] + +The act of adjustment may conveniently be effected by the arrangement +shown in Fig. 72, in which each cross-girder is hung up at its centre by +four bolts. At the middle of the centre girder the total amount to be +screwed up will be that corresponding to the deflection excess _s_, but +towards the ends this amount decreases, and may advantageously be +represented by a diagram as Fig. 73, in which, if _s_ represents to +scale the amount to be screwed up at a centre cross-girder, the +corresponding amounts for other girders may be read off direct. It will +be apparent that it must be necessary to place the centre girder at +such a height as to leave a space between the old and the new work +greater than the amount to be screwed up, this excess clearance being +ultimately filled by a packing. + +The precautions to be observed in carrying out this kind of work, and +the practical methods of adjustment adopted by the author after some +little experience, may here be given. + +Great care is necessary at the outset to ascertain the true spacing of +the cross-girders, to ensure that the bolt-holes in the bottom flange of +the centre girder shall come where desired. The fixing of the +cross-girder brackets also needs close attention to avoid after trouble, +the bolt-holes in the brackets being preferably drilled on the site +after fixing. It will, for masonry abutments, be necessary to fix +bedstones to receive the new centre girder, which, being carried out +quite possibly under adverse traffic conditions, will perhaps leave the +stones liable to settle slightly when the full load is carried. To +eliminate the bad effect of this upon the ultimate adjustment, and to +take up any initial set of the new girder work, which would be +prejudicial in the same way, it is desirable, the centre girder being in +place, to screw up the bolts temporarily and leave the work for a week +or two. To ensure regularity in the screwing up process, it is +convenient to prepare, for use at the bridge, a diagram somewhat similar +to Fig. 73, giving the amount by which the new and old work are to be +brought together at each cross-girder, with the number of turns for each +nut to effect this. With a man at each side of the girder, the whole +length is traversed, giving a half-turn to each nut; this is repeated as +often as necessary, and so managed as to bring all up proportionately to +the final requirement, keeping tally with chalk marks over each +cross-girder as a check. The preliminary screwing up should be conducted +with little less care than that adopted for the later adjustment, to +avoid damage to the old work. This later adjustment having in due course +been effected, it is then necessary to measure for packings to fill the +spaces remaining between the old cross-girders and the new centre +girder. These spaces should be callipered at each of the four corners, +care being taken to avoid after-confusion. The measurements ascertained +will, however, be too great for the finished packings, as an allowance +of not less than 1/10 inch (total), will commonly be wanted to cover +irregularities in the surfaces. The packings, having been prepared and +checked, may be slipped into place after slacking all the bolts a small +amount to permit this to be done, finally screwing up tight and securing +the nuts by split-pins, through holes drilled as the last operation. + +As a check upon the calculations and adjustment, the “lift” of the outer +girders and cross-girders, and the “drop” of the centre girder may be +observed by levelling. For this purpose the author has used a staff of +inches divided into tenths, with which, and a good level, very accurate +readings may be taken for short distances. + +No reference has been made to the effect of skew in a bridge on the +above methods, the explanation given applying rather to bridges square +on plan. The influence of skew on the load distribution will largely be +a matter of detailed calculation. The flexure of the girders may also be +sensibly affected, but may be arrived at with sufficient accuracy +without any great trouble. The chief effect of skew is to modify the +amount of screwing up during adjustment, which may be better understood +by reference to Fig. 74, and comparing it with Fig. 73, the adjustment +diagram for a square bridge. + +To illustrate how these methods of strengthening work out, and compare +as to weights of centre girders required, the case has been assumed of a +wrought iron bridge of 60-feet span, having outer girders 5 feet deep, +of 39 square inches gross flange area; and cross-girders, at 8-feet +centres, 27-feet span, 1 foot 9 inches deep, with a gross flange area of +twenty square inches. The dead load and live load on either road are +each 1·75 tons per foot run. + +The stress in the outer girders previous to the alteration being 6 tons +per square inch gross, it is desired to relieve this to the extent of 33 +per cent. by a steel centre girder. In the table here given the +quantities given in italics are fixed as primary conditions:-- + +CENTRE STRENGTHENING GIRDERS FOR 60-FT. SPAN. + + ----------------------------+-----------+------------+------------ + | Centre | Centre | + | Girder, | Girder, |Adjustments + ---- | Stress | Depth | Unknown. + | Unknown. | Unknown. | + ----------------------------+-----------+------------+------------ + _Outer Girder._ | | | + | | | + Deflection under modified | | | + live load | ·42 in. | ·42 in. | ·42 in. + Lift of adjustment | _nil_ | _nil_ | ·153 „ + | | | + _Cross Girders._ | | | + | | | + Depression under live load | | | + --modified conditions of | | | + support | ·13 in. | ·13 in. | ·13 „ + Extreme depression (_m_) | ·55 „ | ·55 „ | ·55 „ + Lift of adjustment (cross- | | | + girder only) | _nil_ | _nil_ | ·095 „ + Total lift of adjustment | | | + (_l{t}_) | _nil_ | _nil_ | ·248 „ + | | | + _Centre Girder._ | | | + | | | + Depth | _3·5 ft._ | 8·2 ft. |_3·5 ft._ + Unit stress on gross section| | | + (ex girder’s weight) | 2·14 tons | _5·0 tons_ |_5·0 tons_ + Total deflection (ex | | | + girder’s weight) | ·55 in. | ·55 in. |1·28 in. + Deflection excess (_s_) | _nil_ | _nil_ | ·73 „ + Depression, or “drop” of | | | + adjustment (_d{t}_) | _nil_ | _nil_ | ·482 „ + Gross area of flange |105 sq. in.|19·2 sq. in.|44·5 sq. in. + Weight | 20 tons | 10·4 tons |11·4 tons + Net flange stress (including| | | + girder’s weight) | 3·19 tons | 6·87 tons | 6·94 tons + ----------------------------+-----------+------------+------------ + +Girders subject to distributed load are treated as having uniform +stress, but where this is not strictly the case, as in some light +girders, it will be necessary to take the fact into account. For centre +girders of wrought iron, and a unit stress on the gross section of 4 +instead of 5 tons, the girder weights are between 9 and 10 per cent. +greater. + +[Illustration: FIG. 74.] + +In the above treatment of the application of centre strengthening +girders there is a source of error which should be touched upon. If, +under live load, the centre girder deflects more than the outer girders, +as it commonly will, there must be a want of uniformity in the behaviour +of the cross-girders, those near the abutments being more relieved than +the estimated amount of relief of those at the centre, which will have +less than that intended; but the reduction of stress in the +cross-girders will generally be so considerable that any such ambiguity +of excess or defect is commonly unimportant; the effect of this also +upon the main girders is much less than might be supposed, being, for +the third of the cases just given, about 2-1/2 per cent. excess for the +centre girder, and generally a much smaller error. With this +qualification, the method can, however, be regarded as approximate only. +It is possible to eliminate some part of the error by lifting the end +cross-girders during adjustment, a less amount than that given by the +diagrams, Figs. 73 and 74, taking care that the centre girder is +depressed its full amount by lifting the centre cross-girders a little +more; this refinement is hardly necessary, and unless controlled by +calculation cannot be depended upon for precise results. + +Particulars are here given of five ordinary cases, comparing the +calculated and observed results of adjustment. The operation of +levelling was conducted by a quick-eyed and capable assistant, who was +not made acquainted with the results expected, in order to avoid any +sub-conscious tendency to match the calculated figures:-- + +EXAMPLES OF CENTRE GIRDER ADJUSTMENTS. + + ---------------------------------------+-----------+----------------- + -- |Calculated.| Observed. + ---------------------------------------+-----------+----------------- + | in. | in. + | | + No. 1.--56-_Ft. Span._ + | | + Depression of centre girder | ·82 | ·84 + Lift of cross-girders at centre | ·23 | ·22 + Lift of outer girders | ·20 |·10 and ·13 + | | + No. 2.--57-_Ft. Span._ + | | + Depression of centre girder | ·50 | ·50 + Lift of cross-girders at centre | ·18 | ·20 + Lift of outer girders | ·11 |·08 and ·10 + | | + No. 3.--67-_Ft. Span._ + | | + Depression of centre girder | ·70 | ·75 + Lift of cross-girders at centre | ·15 | ·17 + Lift of outer girders | ·10 | ·09 + | | + No. 4.--68-_Ft. Span._ + | | + Depression of centre girder | ·70 | ·65 + Lift of cross-girders at centre | ·20 | ·18 + Lift of outer girders | ·13 | ·14 + | | + No. 5.--52-_Ft. and_ 28-_Ft. Spans continuous._ + | | + |Long |Short|Long |Short + |Span.|Span.|Span.|Span. + ---------------------------------------+-----+-----+-----+----------- + | in. | in. | in. | in. + Depression of centre girder | ·28 | .. | ·29 | .. + Lift of centre girder | .. | ·04 | .. | ·03 + Lift of cross-girders (centre of spans)| ·17 | ·09 | ·15 | ·13 + Lift of outer girders | ·08 | .. | ·08 | .. + Depression of outer girder | .. | ·01 | .. |negligible. + ---------------------------------------+-----+-----+-----+----------- + +The method of calculation adopted for these cases was not precisely that +given, though depending upon the same broad principles. The first cannot +be considered a good example. The last, having continuous girders, of +course needed special treatment. + +Of about seventeen bridges strengthened in the manner described, the +effect generally was satisfactory, in reducing deflection and vibration; +but in two cases of small span, owing probably to settlement of +bedstones, the results were not so good. + +From first to last the work of putting in a centre girder takes some +little time, owing to the slow progress generally made in fixing the +brackets, preparing packings, etc. The cost of a typical case was about +23 per cent. of the cost of a new superstructure, with a 30 per cent. +relief of stress. + +[Illustration: FIG. 75.] + +[Illustration: FIG. 76.] + +A special case of strengthening by a centre girder, having considerable +interest, may be here referred to. The primary idea involved was not the +author’s. The bridge dealt with has already been noticed under “Bracing” +and a section, before alteration, shown in Fig. 26. The span being 85 +feet, there was no room for a centre girder of sufficient depth above +the cross-girders and between the roads, nor was it considered +economical to place the girder wholly below the floor, because of the +costly staging this would have necessitated for erection purposes, the +height above ground level being very great. A girder was therefore +designed, having open latticing at an angle of 60 degrees, with a bottom +boom to be below the cross-girders, the top being as high above the +rails as could be permitted (see Figs. 75 and 76). A temporary boom was +arranged at the intersection of diagonals, the lower boom proper not +being fixed till the girder having been lifted into place, with the +diagonal members passing between the cross-girders, allowed this to be +done. The girder for some time carried itself from bearing to bearing, +with the temporary boom in tension, the deflection being then 2 inches. +The permanent boom was then put in place, and the girder restored as +nearly as was practicable to the camber it was intended to have when +complete, but without throwing, during the process, any improper loads +upon the old work. + +The lower boom being finally riveted up, the cross-girders were made to +bear upon it by suitable packings. There were, in addition to the new +girder, two stiff frames between the old main girders, to which the new +was secured. + +The girder was designed with the intention that under dead load only the +cross-girders should just rest, but throw no weight, upon the new work, +the latter assisting to carry live load only. The floor beams being of +small span, and securely riveted to the old girder tops, the centre +girder was required to deflect, under its share of live load, the same +amount as the old main girders under the remaining portion, the three +points of support of the cross-girders thus not altering their relative +levels. That this resulted was evident from the fact that, previous to +connecting the cross-frames to the centre-girder, the work being +otherwise complete, a space between the two of about 1/2 inch, +afterwards filled by a packing, showed no alteration, the closest +measurement failing to disclose any relative movement upon the passage +of live load. The reduction of vibration was, as might be expected, very +marked. + +In the conduct of that class of strengthening work which has been dealt +with in this chapter, it is essential, in the author’s judgment, that +the man responsible for the detailed calculations and design should +himself see the operations of adjustment carried out, or delegate it +only to one equally familiar with the requirements. + +Before dismissing the subject, it will be well to refer to a method of +approximately determining flexure curves, of occasional use in dealing +with centre girder or similar questions. The figure assumed is plotted +to an exaggerated scale, with which object the actual radius of +curvature at points along the girder’s length are first ascertained by +the formula + + E × D + ------- = R, radius of curvature in feet, + _f_ × 2 + +and the radius of curvature for the diagram by + + 12 × R × F^2 = _r_, radius for plotting, in inches (5) + +E being the modulus of elasticity, D the girder’s depth in feet, _f_ the +mean of the extreme flange stresses per square inch of gross area, and F +the fraction indicating scale as 1/48, where 1/4 inch = 1 foot. The +curve, being plotted, shows by direct scaling the movement of any point +relative to its original position. Near the ends of the curve where the +radii may be of considerable length, the arcs may be drawn with the help +of template curves, or even set out as pieces of “straight.” + +When the curve is laid down so that its chord equals the span to scale, +the method involves an error of excess in the resulting deflection or +droop which is as much as 7 per cent. when the mean radius for plotting +equals the span as drawn, or when the droop of curve approaches +one-eighth of the span. As the exaggeration of curvature is made less +pronounced, this error rapidly diminishes, till for a droop of about +one-sixteenth the percentage is one-fourth part of that above given. +This excess in the droop of curve may be amended by the following +expression:-- + + (droop^3 ) + droop - (------- × 3·73) = corrected droop, or deflection. + (chord^2 ) + +For some purposes it may be preferable to amend the radii for plotting, +so that the curve, as laid down, shall be correct, which may be +effected by the formula here given, to be applied to each value of r, as +first ascertained:-- + + (chord^2 ) + _r_ + (------- × ·0625) = corrected plotting radius. + ( _r_ ) + +If, however, the length of curve is made equal to the span (the chord +then being less), and the radii for plotting as given by (5) are used, +the result will for most purposes be sufficiently precise, though there +will now be an error of a contrary kind, which, for a curve having a +droop of one-eighth, will be about 2 per cent. too little. A somewhat +similar method of setting out deflection curves is described by +Professor Fleeming Jenkin in the article “Bridges” of the “Encyclopædia +Britannica,” but without corrections. + +A careful comparison of results by the above means, with those +calculated, shows that with good draughtsmanship they may be relied upon +for considerable accuracy. Equally applicable to girders of varying +depth and flange stress, they have also a limited use in cases of +continuity. + +[Illustration: FIGS. 77 and 78.] + +Figs. 77 and 78 illustrate the deflection and stress diagrams for the +cross-girders of the bridge supposed to have been strengthened by a +centre-girder, when under the influence of live load and a centre +reaction of a definite amount. As a matter of convenience, each radius +length has been halved, before correction, so that the resulting droop +of the curve is twice the true amount. + + + + +CHAPTER XII. + +CAST-IRON BRIDGES. + + +Cast Iron as a material for bridges has of late years fallen into +disrepute. It is now entirely tabooed by the Board of Trade for railway +under-bridges, unless of arched construction. This condemnation of cast +iron followed, and was apparently the result of, an accident which +occurred to an under-bridge on one of the southern lines, which bridge +had already earned for itself an ill repute by breaking down on a +previous occasion. The ultimate issue was, however, good, inasmuch as it +led to a thorough overhaul of all railway under-bridges in this country, +and the renewal of a great number no longer in a condition suited to the +carriage of heavy or of passenger traffic; yet there is little doubt +that, in the author’s judgment, many excellent cast-iron bridges were +then removed at considerable cost, to be replaced by others of wrought +iron or steel, which will not last so long as many of those displaced +had done, or would still have lasted had they not been dismantled. + +The earlier cast-iron bridges were commonly made of cold-blast iron, a +material of such strength and toughness as to give an extraordinary +amount of trouble in breaking up the heavier parts, when the time +arrived to do this, and with which material ordinary hot-blast iron is +not to be compared for reliability. + +[Illustration: FIG. 79.] + +As illustrating the very considerable stress to which cast iron may be +subjected, without of necessity leading to any mishap, two cases may be +cited. The first, a bridge of 32 feet effective span, carrying two +lines of way, each pair of rails being supported upon Barlow rails, +forming the bridge floor, the ends resting upon the bottom flanges of +inverted [T]-shaped girders, 2 feet 3 inches deep, as shown in Fig. 79. + +The extreme fibre stress works out at 2·9 tons per square inch in +tension, and 5·9 tons per square inch compression, calculated as it +would be in ordinary office work; but for the actual loads, at a span as +above, exceeding the clear span by 6 inches only, and without regard to +the effects of eccentric application of the load. The girders when taken +out showed upon examination no sign of overstrain. The practice of +loading cast-iron girders in this manner cannot, however, be too +strongly condemned, notwithstanding that in this case no ill resulted. +It is evident that a piece of the lower flange being broken out from +this cause, as occasionally happens, might so reduce the section as to +result in complete failure. + +[Illustration: FIGS. 80 and 81.] + +The second example is that of a small railway under-bridge of two spans, +continuous over the central pier, each span being 16 feet 6 inches. The +rails were supported upon longitudinal timbers lying within +trough-shaped girders, as shown in Figs 80 and 81. + +The stress over the pier, in the extreme fibres of the top flange, is +estimated at 4·7 tons per square inch in tension, but it should be noted +that the effect of the timber longitudinal and rail has been neglected +in arriving at this result, which might possibly on this account be +reduced to near 3 tons per square inch. + +The case is noticeable because no evidence of high stress was apparent. +The author saw nothing to suggest sinking of the central pier, the +effect of which, within limits, would be to further reduce the stress as +calculated; but it is quite possible some slight settlement had +occurred; this, as the spans were so small, would have a sensible +effect. While too much reliance should not, it is clear, be placed upon +any estimated result about which there is a lingering doubt, it should +be remarked that, as it would be necessary the pier should sink 3/16 of +an inch, for each ton of reduced stress, it is not probable that the +results quoted are in excess to any material degree; they are, indeed, +more probably low, as no notice has been taken of impact. + +Though cast-iron girders for railway under-bridges are now prohibited in +this country for new works, there are still uses to which they may be +applied, and it may be well to insist that girders of this material +should be fairly loaded, the weight being brought upon them in such a +way that there shall be no serious secondary stress, such as arises when +wide flanges are made to carry concentrated loads; the author has, +indeed, met with no instance of a cast-iron girder breaking down under a +load fairly applied. Preference is now given to steel or wrought iron +for columns; while this is often quite justifiable, there remain many +cases in which nothing better need be desired for this purpose than good +cast iron, provided only that the column be loaded in a suitable +manner--i.e., axially, and that the arrangement and details of the +super-structure are such that there shall be no cross-breaking efforts, +or rocking of the column due to temperature or other causes; unless, +indeed, such cross-breaking or rocking is definitely taken into account +in designing the work. The same care observed in the detailing of +cast-iron work that is not infrequently taken in the design of +structures made of rolled sections would, in suitable cases, the author +has no doubt, yield results just as reliable in practice, with the +advantage of greater resistance to rust, and a reduced cost in +maintenance. + +Good cast iron is, in fact, when used with discretion, a most excellent +material, popular predjudice notwithstanding. The oldest metallic bridge +in this country at the present moment is of that metal. + +The one chief respect in which cast iron is at a disadvantage compared +with wrought iron or steel is that it does not give premonitory warning +of failure--it remains intact, or it breaks. The indications of +weakness, which may be read by an experienced inspector of other +metallic bridges, are in a great measure absent. There is also an +objection which may exist, but is to be avoided by good design and care +in the foundry--viz., internal stress due to unequal cooling. In extreme +cases this may lead to fracture before the work has left the maker’s +hands, but it can only occur by neglect of ordinary precautions. + +[Illustration: FIGS. 82 and 83.] + +In a case which has already been referred to in the chapter on +“Deformations,” page 80, an outer rib of a cast-iron arch fractured near +the crown after fifty-four years’ use. Owing to the nature of the +design, and the fact that the near abutment had closed in slightly, +bringing the linear arch of necessity near the lower edges of the arch +segment in question, it was possible to estimate, with a probability of +truth, the extreme fibre stress (tensile) due to the load forces, at the +upper edge where fracture commenced. The result was very far from +explaining the occurrence of the break, but an examination of the +details shown in Figs. 82 and 83 will make it apparent that, in addition +to the tensile stress, as calculated, there was probably a severe +initial stress of the same character due to irregular cooling in the +foundry half a century before. The sum of these stresses, it is +suggested, placed this particular casting in a critical condition, such +that operations in the construction of a new bridge adjacent either by +producing a small further settlement of the foundations, of which the +author saw no evidence, or, as is more probable, the attachment of a +rope to this rib for the purpose of keeping a barge in position, which +certainly did occur, gave the arch rib just such an additional strain as +to result in the break shown, though no one of these causes acting +singly would have been sufficient to induce fracture. The inner ribs +were of a much less objectionable section. + +[Illustration: FIG. 84.] + +Cast-iron arches, though still allowed by the Board of Trade rules, are, +indeed, liable to be seriously affected by settlement, or yielding of +the abutments, unless hinges at the crown are introduced. As an instance +of this may be quoted a bridge of some 45 feet span, in which the arches +were cast in two pieces abutting, and very efficiently bolted together +at the crown, the springing and vertical abutment member of the +spandrel being bolted and built solidly into heavy masonry. The arch +sank at the crown, caused by, or itself the cause of, a movement of the +abutment, with the result that the lower bolts at the crown joint broke +away, rupturing the casting, as shown in Fig. 84. The arch must then +have acted as though hinged at the crown, as effectiveness of the +connection was destroyed. It had been better, evidently, if a proper +hinge had originally been provided. The break happened to occur so as to +leave a sufficiently good bearing face at the crown; there was, indeed, +no tendency for one surface to slide upon another; but in the accidental +fracture of cast iron this cannot be assured, and the liability to it is +a risk which should be eliminated if possible. + +A second case of very much the same character has also been under the +author’s observation, though in this the ends of the spandrels were not +built into the brickwork of which the abutments were composed. Other +instances of fracture either in the arch proper or in the spandrel work, +have come under notice, though particulars cannot now be adduced; but +the examples cited are by themselves sufficient to justify the +conclusion that it is imprudent to construct a cast-iron arch without a +central pin or its equivalent, unless the abutments, being exceptionally +well founded, may be relied upon as free from any liability to move. It +is, however, to be borne in mind that movement in the abutments of a +small arch of any given absolute amount is more injurious than the same +amount of movement in the abutments of large arches of similar design, +so that what may be negligible in the latter case would perhaps be +destructive in the former. + +To the absence of ductility and liability to initial stress must be +added yet another disadvantage to which cast-iron work is prone--viz., +the possibility of concealed defects, blow-holes or cold-shuts; these in +good foundry practice are not very likely to occur, but, as they are +possible, cannot be overlooked in considering the suitability of cast +iron for bridgework, or, indeed, any structural work liable to serious +stress, and particularly tensile stress. With these remarks by way of +qualification, the author reiterates his opinion that there is still a +use for cast iron in bridgework. + +With respect to the repair of cast-iron bridges, but little is to be +said; the possibilities in this direction are very limited. Occasionally +it may be desired to deal with the fracture of some member in the +spandrel bracing of an arch, when it is commonly sufficient, and even +preferable, to limit the repair work to confining the fractured parts in +such a way as to prevent displacement. + +Rarely it may happen that an arch fractures as a result of settlement, +or other movement, when, if it is decided that safety of the structure +is not imperilled, it will in this case also be preferable to confine +the parts simply by flitch-plates or other contrivance, with no attempt +rigidly to make good the break, the consequences of which treatment +would probably be to induce fracture in some other place. Effective +strengthening of a cast-iron structure is seldom practicable, though +something may occasionally be done by the negative process of lightening +the dead load, or by remodelling the permanent way. Arches may, however, +be rendered much more reliable by the introduction of suitable bracing +where this is either wanting or inefficient. + +In scheming such additions it is desirable to arrange for as little +drilling of the old work as is possible; where this cannot be altogether +avoided, the position of the holes should be carefully chosen with +regard to the effect they may have upon the strength of the old work. + + + + +CHAPTER XIII. + +TIMBER BRIDGES. + + +Timber bridges, though probably the most ancient in type, are yet the +least durable in any particular instance. The perishable nature of the +material when used for exposed construction renders it peculiarly liable +to develop defects which quickly put a limit to the life of the +structure. In addition to decay in the body of the main members--which +may perhaps be long delayed, so that a simple beam bridge may last for +many years--there is in more complex designs decay at connections and +joints, which proves very detrimental to the integrity of the whole. +Water running upon the surface of a member gravitates to its lower end, +and, if there be a joint or other connection, settles there, to be +productive of lasting mischief. From this cause, together with a very +common deficiency of bearing surface relative to the forces to be met, +the joints soon develop some movement; working of the structure +commences under passing loads, its final destruction being then a +question of time only. Each joint is, in fact, in timber bridge +construction a source of serious weakness to a degree which has no +parallel in well-designed metallic bridges. + +Wrought-iron straps to confine the ends of raking members, or for other +uses, are liable to crush into the wood, and bolts are apt to enlarge +the hole through which they pass. Wood keys, where these are introduced +to prevent one timber from sliding upon another, are also prone to +develop cracks in the main members, and fibre crippling from excess of +stress. All these defects are, however, in timber-work more easily +defined than efficiently remedied, as it is barely practicable for any +but the harder woods to ensure, for heavy loads, a sufficiency of +bearing surfaces. + +The most readily detected evidence of deterioration in timber bridges is +the sag of its bearing members, or trusses, for the simple reason that +if there is no local trouble at the joints, there will probably be no +appreciable drop at the centre of the span. The existence of such a +depression may, however, be caused in rare instances by the spread of +the supporting piers or abutments, particularly in the case of beams +trussed by end diagonal rakers and having no tie. + +Bridges formed of deep trusses, with the road upon the top, are +sometimes found to be wanting in lateral bracing, the result of which is +that the main trusses go out of line, leaning considerably one way or +the other, being checked only by such rigidity as the joints and +floor-beam attachments may have, with possibly some assistance from the +end connections of the span. + +The decay of piles where entering the ground or water is, of course, a +fruitful source of trouble, as also is the sinking of piles, where these +are insufficient in number, or have not been well driven in the first +place. + +A vital difficulty with timber structures generally is the uncertainty +that will commonly exist as to how far decay extends in those cases +where it has started. Timber does not necessarily show upon its surface +the evidences of internal rotting. Memel timber may, indeed, be +sometimes found to have become thoroughly unreliable, yet showing no +sign of this upon its painted surface. By sounding the wood with a +hammer, or by probing, its condition may commonly be ascertained. In +cases of doubt, an auger-hole will make it clear as to whether the +interior be good or otherwise, as to the particular parts tested; but +only as to those parts, leaving it a matter of guesswork as to the +remainder. + +[Illustration: FIG. 85.] + +A railway bridge having many of the defects which have been indicated +may be quoted as an example. This structure crossed a canal, supported +upon piles, some of which were in water, others carrying land spans. The +canal span consisted of four trusses, one under each rail, or nearly so, +framed in the manner shown in Fig. 85, precise details not, however, +being now available. The trusses, apart from deflection under live load, +sagged considerably--in one instance, 4-1/2 inches; one inside truss was +also leaning towards the centre line of the bridge as much as 3 inches. +One raker, or diagonal strut, was rotted half through its thickness, and +many other timbers were badly decayed. The end connections and joints +were also in a bad condition. The vertical tie-bolts of the main trusses +were all slack. The piles generally, many of which were badly decayed, +had sunk and inclined towards one end of the bridge about 4 inches in 7 +feet of height, the ground being soft and unreliable. + +Movement under a passenger train crawling over the bridge was very +appreciable, but not startling. There had been introduced, from time to +time, additional timbers and iron ties, with the object of rendering the +spans more reliable, but leaving it somewhat difficult to determine the +function of the several members. The bridge was, of course, +reconstructed. + +[Illustration: FIG. 86.] + +[Illustration: FIG. 87.] + +[Illustration: FIG. 88.] + +An instance may here be cited showing how badly distorted a timber +structure may become without actually falling. The bridge referred to +consisted of three spans of 29 feet, each span having two trusses, +between which ran a colliery tramroad, 1-foot 6-inch gauge; the corves +running upon this, at 4 feet 6 inch centres, weighed, when full, about +10 cwt. each. The trusses were badly out of shape, the centre span +having sagged 5-1/2 inches, with one truss of the same span nearly 10 +inches out of line at the centre. This little bridge, of which some +details are shown in Figs. 86, 87, and 88, had been in use about twenty +years. + +[Illustration: FIG. 89.] + +A third case which may be named is that of a road bridge, about 12 feet +wide, crossing by thirteen spans a shallow river liable to floods. The +construction was of a simple character, as indicated in Fig. 89, and +consisted of piles supporting trussed beams, which had sagged in some +instances over 2-1/2 inches. The bridge had, some years previous to the +author’s inspection, been heavily repaired, many new strut and +stretching pieces having been introduced, the piles also being +reinforced or renewed. Five years before, a traction engine, said to +weigh 5 tons, had passed across the bridge in safety; but the author +noticed that a coal wagon, which, with the horse, weighed about 50 cwt., +when walked slowly over set up much movement. This bridge had been in +use nearly thirty years, and was very much out of line from end to end. + +Though timber bridges cannot at the best be considered durable, yet, by +attention to certain points in design and construction, their length of +life may be materially enhanced. Every cut across the grain may be +considered an element of weakness by exposing the material to quicker +decay, for which reason the number of ends, or of joints, should be +reduced to a minimum. An additional reason for reducing the number of +joints or other connections is the liability of these to develop +movement, as already stated, the yield of any one joint, being the cause +of movement in others, which might, but for this, have remained close. +These considerations lead to the conclusion that fewness of parts is, in +timber construction, as in structural work generally, an excellent +principle to observe. Mortising, elaborate scarf joints, recessing, or +any cutting into the timber which is not essential, should be avoided, +the simplest forms of connection being preferable, if at all suitable. +If a step or butt surface is wanted for any member, it is commonly +better to provide this by a cleat or other added piece, rather than by +cutting into the timber butted against. + +A complicated joint formed in the body of main timbers can only be +renewed by renewal of the timber itself, whereas by the method indicated +the joint is readily tightened, or re-made, without involving the main +member. Bearing surfaces should be ample, straps of liberal dimensions, +and bolts large (with good washers), both for the sake of bearing +surface in the holes, and reduction of any liability to bend under +cross-stress. In trusses of the form shown in Figs. 85 and 86, it is +desirable to introduce diagonal members in the middle bay, even though +it may appear that the stiffness of the main beams is sufficient to +render this unnecessary as a matter of strength, as without these there +is apt to be, under rolling load, a slight distortion, leading to +working of the joints and free entry of moisture. Lateral bracings +should also, for much the same reasons, be introduced, even though they +may not appear necessary in the new structure, with joints all close and +effective. + +Projecting ends of timbers should be carried out well beyond the +requirement of strength or bearing, in order to ensure a liberal margin +for that decay in the end fibres which commonly develops. Timbers +resting upon abutments, or running into confined spaces, should be +arranged for free ventilation and ready drying. Occasionally joints at +the lower ends of timbers are protected by lead or zinc flashings to +prevent water running into them, a method which should have some +protective value. Whatever measures may be adopted, whether in the +design or execution of timber bridge-work, will, however, be but little +effective, if the timber itself is not good of its kind, and well +seasoned. + +Creosoting to be useful should be thorough and something more than skin +deep. The timber itself should be well dried before treatment. + +The repair of timber bridges very largely consists in the renewal of +decaying timbers, where this is practicable, or in adding supplementary +pieces where the old cannot conveniently be displaced. Joints may be +tightened up by hard-wood wedges, properly secured to prevent slacking +back, all bolts being also screwed up tight, perhaps some additional +being introduced. + +Piles standing in water, which have decayed, may be strengthened by +driving other piles between the old, or on either side, but not of +necessity opposite to them, and by means of waling timbers bolted to the +old piles, put in a position to take load, either by the walings resting +upon their tops, or being bolted to them. Piles decayed where entering +solid ground may generally be strengthened by bolting on supplementary +timbers to reach well above and below the decayed part, or by cutting +out the bad length, introducing a new piece, and fishing the butt-joints +in a proper manner. But all remedial measures have generally to be +considered with reference to cost, as compared with the probable +increase of life of the structure. With a bridge in an advanced state of +decrepitude, such repairs may prove anything but economical, and at the +best defer reconstruction but a very moderate length of time. + + + + +CHAPTER XIV. + +MASONRY BRIDGES. + + +Masonry bridges, in which description it is intended to include +structures both in stone and brick, are, when well built, amongst the +most durable and long-suffering of any which come under the care of a +maintenance engineer; yet when developing the faults peculiar to their +kind, they may be the occasion of much anxiety, and render necessary +frequent inspection, or even continuous watching. + +Apart from decay of mortar or material, defects may very commonly be +traced to the foundations, or to earth-slips. Sinking, when uniform, may +be quite harmless, though possibly inconvenient; irregular sinking of +piers or abutments is quite a different matter. It is, however, +remarkable to what a degree sinking may be evident, without of necessity +rendering a structure unsafe. Movement of an amount and kind which would +be fatal to the connections of metallic bridgework is endured by bridges +of stone or brick; not, it may be, without damage, yet with no occasion +for alarm. The superstructure of metallic bridges may often, however, be +restored to the true level before the mischief has become serious, +whereas in the case of masonry arches this is not practicable. + +Spreading of the abutments is very seldom the cause of any great injury +to an arch, though it is common enough to find old and flat arches +slightly down at the crown; but the contrary case of abutments closing +in is not very unusual when these are high, or terminate a viaduct over +a deep valley. Such an abutment may move during or soon after +construction, throwing up the crown of the end span affected; or, if the +arches are very solid and heavy, the abutment may slide forward at the +base, with no sensible reduction of the opening. + +When a viaduct connects the two ends of a high embankment, it may happen +that the end piers are not clear of the embankment slope, in which event +a pier may, should the bank slip, move with it, as to that part not in +solid ground; with the result, in a bad case, that it is broken across +and the superstructure imperilled. + +[Illustration: FIG. 90.] + +A case of abutment movement is illustrated in Fig. 90, which represents +the end arch of a masonry viaduct, one abutment of which had moved +forward in the manner already referred to. From the springing upwards +the arch retained its form to within a short distance of the crown, +where it was forced up in the way indicated. When the movement became +pronounced, heavy timber centering was introduced, with the object of +preventing any mishap, the damaged portions being ultimately cut out and +made good. The structure was thirty-five years old. + +The practical utility of stop piers in long arched viaducts is, perhaps, +rather in checking movement of the tops of piers under moving load than +in arresting actual failure of a series of arches. That the tops of +piers do move very sensibly need not be doubted. The author has +attempted to measure this in the case of piers about 60 feet to the +springing, by means of a theodolite placed below, but has reached no +more definite result than that a movement existed, of which he was not +able to determine the amount. If in a viaduct some arches are more +heavily loaded than others, each spreading slightly, the end piers of +the group will move amounts which together equal the sum of the +individual span spreads, with a tendency in the arches beyond those of +the group overloaded to rise. + +This rocking may be detrimental both to the piers and arches, and helps +to account for the disintegration of mortar in arches and piers, which +not infrequently happens. The soffits will sometimes be seen with a +thick incrustation of lime, which has washed out of the joints, or from +limestone ballast above, where this has been in use. Arches of tall +viaducts may, indeed, become in so bad a condition that pieces of stone +or brick will drop out, necessitating repair at heavy expense, of which +scaffolding is commonly a large part. + +Tall piers may be found badly out of the upright due to sinking of +foundations. A marked case of this kind came under the author’s +notice--a viaduct of fifteen semicircular arches, in which, though many +piers were wanting in truth, one in particular was about 1 foot 4 inches +out of vertical, making one side of the shaft plumb, and doubling the +normal batter of the other. Inquiry showed that in this instance the +pier had never been upright from its earliest history dating back +thirty-six years. This makes clear the desirability, to avoid hasty +conclusions, of ascertaining, when it is possible to do so, the complete +record of any structure. + +A bridge fifty-eight years old, of three skew spans, carrying a railway +over a canal, and having somewhat flat brick arches with stone quoins +upon low piers, developed the somewhat unusual defect, as to the centre +arch, of splitting along its length for about 10 feet, parallel to and +some 7 feet from one face. In this case there was reason to believe that +there had been considerable local settlement of the piers on that side +of the bridge. The arches were otherwise in bad condition, the brickwork +poor, and the mortar decayed. Each arch was down at the centre, and +displayed a fault not unusual where bad brickwork joins up to good cut +stonework, the quoins showing a tendency to separate from the brick +rings. Below the bridge were coal-workings. + +Brick arches built in parallel rings sometimes separate one ring from +the other, demonstrating the known propriety of bonding the rings +together properly, and of carrying the arch round, when building, at its +full thickness. + +[Illustration: FIG. 91.] + +An instance of bridge failure from a somewhat peculiar cause may be +quoted as of some interest, largely because the structure was very +ancient, having been in existence some 400 years. This bridge, carrying +a road, was of the type usual in old masonry bridges over a river, +having small arches, thick piers, and solid backings to the arches. Two +flood-openings at one end had, by sinking and want of care, become +partly closed. The centre arch had, however, been widened about 140 +years previously. During a severe flood, the swollen river, overflowing +its banks, trespassed upon a timber yard a little above bridge, and +washed down into the stream a large quantity of sawn timber; this, +unable to get through the main arch with freedom, compacted into a +serious obstruction. The flood water, thus checked in its passage, seems +to have scoured below the timber, and robbed the piers of such support +as they formerly had (see Fig. 91). The bridge stood in this condition +till the water lowered, when the middle part of the structure broke up, +and subsided into the hole which had been washed out. But for the +monolithic character of the old work it is probable the bridge would +have failed long before, as the gravel bed on which the piers stood had +been partly undermined for very many years. The case is instructive, as +showing how a slight accident--powerless by itself to work mischief--may +be very damaging when allied with so powerful an agent as running water. + +[Illustration: FIG. 92.] + +The enduring character of even the roughest class of masonry arch, if +only the material be good and abutments stable, is shown when it becomes +necessary to destroy old work of this character. Fig. 92 represents a +short length of “cut and cover” arching in process of demolition, just +before it fell in. The masonry was of hard sandstone rubble and had been +cut away, as shown, till at the point A only a very small piece of the +arch remained, when the length finally broke up and dropped. Arches have +commonly a great reserve of strength; tunnel linings are, indeed, often +badly out of shape, closed in, and sunken; yet continue, with close +watching, and occasional repairs where the work has decayed or bulged, +to serve the purpose intended. + +Though the equilibrium of masonry arches has been the occasion of much +profound study, and the nicest calculation has sometimes been applied to +the design of such work, yet it appears that when an arch is well backed +up, the theoretical linear arch need have but little connection with the +figure of the intrados; a statement consonant both with common-sense and +the teachings of experience. With solid backing, this would indeed seem +to be more important than any part of the arch ring below the top of the +backing, the lower part of the ring serving chiefly to preserve the face +of the solid work. Arches are frequently to be met with so out of their +true shape that but for the consideration named, failure would seem to +be inevitable. The masonry or brickwork does not always show evidence of +damage, if the distortion has been slow; suggesting that structures of +this kind have a power of accommodation with which they are not +generally credited. + +A noticeable cause of deterioration of masonry structures, which may be +quite independent of settlement, is serious vibration. This is well +known in connection with church belfries, and is also locally apparent +when telegraph or other poles are attached to masonry parapets. +Vibration, when caused by heavy railway traffic, acting upon arches +light or originally bad, may demoralise the structure to such an extent +that repair becomes exceedingly difficult, because of the extensive +character of the mischief; but masonry bridges substantially built, and +particularly those carrying ordinary roads, and not subject to much +vibration, have great lasting powers, if repaired with skill, or even +let alone. Distortion of the arch may be quite consistent with practical +stability, if the movement or decay with which it originated is not +progressive, or has been arrested. In this connection a distinction is +to be made between arches well backed, to which the foregoing remarks +apply, and in which the two halves of each arch may act as separate +monoliths meeting at the crown, and the case of a true arch ring +independent of any outside resistance, such as backing or spandrels may +give, and depending almost wholly upon the proper balance of its +component voussoirs for its stability. With the latter class of +structure no liberties may be taken; whilst with the former there is +seldom cause for fear, if the foundations do not give way, and the work +is dealt with judiciously, if at all. It must, however, be understood +that there are limits as to what may be done effectively, short of +rebuilding, in dealing with structures in which, perhaps, brickwork is +rotten and mortar decayed and crumbling, the whole being little better +than a broken mass of rubbish. + +In cases where it may be prudent to introduce safety centring, as in an +instance already referred to, it is commonly expedient to refrain from +causing this to take any sensible part of the load till all movement has +ceased, the centres being at the outset largely precautionary. The +requirement with an arch in bad condition is to avoid disturbing it for +the worse. If the centres are wedged up whilst movement is still going +on, the effect may be to cause the arch to break up upon the centring, +and precipitate repair work which might otherwise have been left to a +more convenient time, when all movement had stopped or been checked by +suitable measures. Viaduct arches in a bad condition, but not +necessitating the use of relief centres, are commonly dealt with +piecemeal by cutting out the bad places, a small part at a time, and +making good. The work requires the greatest care of experienced men. + +Pointing masonry or brickwork is effective for little other than +protective purposes, and to check further weathering; it has obviously +no effect upon the interior work, and if made to cover up the evidences +of internal decay, is even misleading and objectionable. In extreme +cases it may be desirable to open out the road and deal with the +filling, to relieve or to strengthen the outer spandrel walls, which +sometimes bulge, or for other purposes, as, for example, for rebuilding +inner spandrel walls, grouting up or otherwise repairing solid backing, +in which operations some regard must be had to the effect of the work +upon the balance of the opposing halves of the arch. + +Of the different classes of masonry commonly used in bridgework, it may +be well to remark that good coursed rubble, or preferably that variety +bonding both vertically and horizontally, of a durable stone, perhaps +quite unfit for any but rough dressing, may make a most lasting +structure, the mortar, of course, being good. Each rough-dressed stone +presents a durable piece, fragments removed separate from the block, +probably along some line of relative weakness--there is no “nursing” of +weak corners; whereas with stones reduced to a perfectly regular shape +by chisel work, the plane surfaces and geometrical angles are made with +partial regard only to the natural grain of the stone. + + + + +CHAPTER XV. + +LIFE OF BRIDGES--RELATIVE MERITS. + + +The life of bridges of differing materials has been incidentally touched +upon by the examples quoted, in dealing with each class of structure. It +will be useful to recapitulate some of the facts adduced, and to compare +the terms of life so far as they appear to be indicated; but in doing +this it is necessary to remember that the life of a bridge of any one +material is inseparably connected with its own private history. The +duration of any such structure may be limited by adverse conditions, +peculiar to the case considered, by defects of design, material, or +workmanship--present from the first--or by neglect, overloading, or +accident, making up its later record. + +With the exception of timber structures, it is difficult to find any +class of bridges furnishing examples which have reached the limit of +life, independently of the evils named, and as a result of unavoidable +decrepitude. There are none the less influences at work tending to this +condition, and which it is too much to expect can in all cases be +foreseen or completely guarded against, such as the shifting or scouring +of river-beds, settlement of foundations, natural decay, and minor +faults in design, which even in the most capable hands may be expected +ever to fall short of perfection. At the best, then, the life of any +structure, though long, must have a limit. With bridges of more average +or inferior qualities the life may be positively short, even without the +destructive influence of overloading. + +Dealing with instances of metallic bridges, the adjacent table gives the +time each had been in existence when removed, and some indication of the +reason for its condemnation. Those marked with an asterisk were cases of +pronounced high stress. From a study of the table it appears that in +actual practice, making no excuses of any sort, the length of life of +the wrought-iron bridges specified varied between twelve and thirty-six +years; but these figures applied to this collection of cases only. It is +to be remarked that many other bridges outlasted these, and are likely +to continue reliable. These results show, then, no more than that some +wrought-iron bridges are short-lived, having, in fact, been selected as +examples of this. Longer-lived exceptions are useful, as indicating that +the durability of such structures is by no means so limited as the table +would suggest. It is to be observed that, as design and maintenance are +now better and more generally understood than when experience was +largely wanting, it is to be expected that later examples will show no +such poor results. + +Of steel bridges little can be said, because of the limited time this +material has been in use; but the generally acknowledged belief, quite +in agreement with the author’s observation, that steel rusts more freely +than wrought iron, suggests that such bridges will have a shorter lease +of life, the more so that the surface-to-section ratio is also greater +for higher unit stresses, though other adverse influences are much the +same for one material as for the other. + +Of cast-iron structures but few cases have been given; of these, +cast-iron arches have been noticed as developing defects which led to +reconstruction, or to limiting the loads to be carried. Plain cast-iron +girders, on the other hand, have never, under the author’s direct +observation, been removed for any other reason than because they were +cast iron, or from over-stress, due to the growth of loads; never from +defects or wasting, though it is not suggested no such cases exist. The +author has no evidence which points to what may be the limit of life of +a good cast-iron girder fairly treated. + +_Examples of Life of Metallic Bridges._ + + -------------------------+-------+------+----------------+------------ + Description. | Span. | Age. | Defect. | Reference. + -------------------------+-------+------+----------------+------------ + |ft. in.|Years.| | + | | | | + _Wrought Iron._ + | | | | + Plate girders | (?) | 12 |Loose rivets | + *Ditto | 35 0 | 12 |Ditto |p. 52 + Ditto | 55 0 | 14 |Rust. Distortion|pp. 78 & 97 + Trough girders | 11 0 | 16 |Loose rivets. |p. 50 + | | |Cracked webs | + Plate girders | (?) | 22 |Loose rivets | + Twin girders | 31 6 | 23 |Weak. Cracked |p. 13 + | | |webs | + Ditto | 35 6 | 23 |Weak. Distorted.|p. 74 + Plate girders | 42 0 | 23 |Loose rivets. |p. 21 + | | |Cracked webs | + Ditto | 72 0 | 29 |Weak. Loose |p. 53 + | | |rivets | + Ditto | 47 0 | 24 |Distortion |p. 9 + Ditto | 32 0 | 32 |Rust. Cracked |p. 14 + | | |webs | + *Ditto | 25 0 | 36 |Weak |p. 63 + | | | | + _Steel._ + | | | | + *Trough girders | 15 8 | 32 |Weak. Rusted |pp. 68 & 98 + | | | | + _Cast Iron._ + | | | | + *Girders | 32 0 | 36 |Weak |p. 141 + Girders, cast-iron piles| (?) | 44 |Ditto | + Arches | 45 0 | 55 |Crack. Settle- |p. 145 + | | |ment | + Ditto |100 0 | 62 |Crack. Deforma- |pp. 80 & 145 + | | |tion | + -------------------------+-------+------+----------------+------------ + +With timber bridges the length of life appears to be about twenty-five +years, but this is very largely dependent upon the question of +maintenance, and may range from fifteen to thirty-five years. It is +manifest that repairs, when extensive and consisting of the renewal of +the more essential parts of the structure, border upon reconstruction, +and may be continued indefinitely. The length of life in ordinary cases, +and for the timbers commonly used in this country, may, for railway +bridges, be taken as stated, though for highway bridges possibly longer. + +Of masonry bridges little is to be said but that it is only in cases of +bad work or material--with, perhaps, vibration or settlement--that these +have a shortness of life comparable with that of defective metallic +bridges. Where these adverse conditions obtain, heavy repairs may be +necessary before the structure is many years old; but, under reasonably +fair conditions, bridges of masonry may be expected to outlast +structures in any other material. Apart from road-bridges which are +admittedly long-lived, there are a large number of railway bridges and +viaducts of masonry which, despite heavy loads and vibration, have been +in use for the past seventy years. + +Dealing with the cost of maintenance, this with bridges of wrought iron +or steel should result simply from scraping and painting, with such +other incidental work as may be necessary on the subsidiary materials +used in the structure. The cost of painting will vary with the height +and character of the bridge, and the amount of scaffolding, if any, and +may be from 5_d_. to 1_s_. or more per square yard; this if distributed +over five years, a not unusual interval between each painting, works out +at an appreciable figure, which may vary from one-third to one per cent. +of the first cost, per annum. The yearly cost of painting steel-work +will, for shorter intervals, come to a somewhat higher figure. Serious +occasional items of expense are those which should not be necessary, +repairs and possibly strengthening, which may raise the total cost of +maintenance very considerably. + +Cast-iron bridges, being less liable to rust, cost less for painting +than other metallic bridges; and if the cast iron is closed in by +masonry, practically nothing; they do, indeed, involve very little +expenditure in the maintenance. Not being very amenable to repair or +strengthening, cast-iron bridges commonly remain very much as built, or +are reconstructed. + +The proper care of timber bridges may become costly as the structure +gains in age, and soon grow to a very wasteful expenditure. This is +evident when it is considered that repairs may be necessary after ten +years, and that whatever may have been the cost of any part when new, it +cannot be replaced for the same amount, having regard to the labour +expended in removing the old member, and the special precautions to be +observed in dealing with an old structure carrying its load. In addition +to ordinary repairs, there will be paint or other protective coating to +be applied, though this is not always done. + +The upkeep charges of masonry bridges will be practically nothing in +favourable cases; but, on the other hand, where extensive repairs become +necessary, may reach a considerable amount. Exceptional outlays are, +however, infrequent, and may be spread over a large number of years, in +those rare instances in which they become imperative. + + _Durability._ _Maintenance _First Cost._ + Charges._ + + Masonry Masonry Timber + Cast Iron Cast iron Masonry + Wrought iron Wrought iron Steel + Steel Steel Cast iron + Timber Timber Wrought iron + +For purposes of ready comparison, placing bridges of the materials under +review in order of durability, they would appear as in column 1 of the +table above; in order of low maintenance charges, generally as in column +2; and in order of low first cost, as in column 3. With respect to the +question of first cost, the arrangement of the third column applies only +to small bridges, say, up to 70-foot span; and, being liable to +variation with the conditions, is but approximately correct. The less +costly descriptions of masonry are alone considered in this connection. + +It may be added that the total yearly charge of interest on first cost, +redemption, and maintenance, appears to be for masonry bridges, about +one-half only of the corresponding totals for bridges of wrought iron, +steel, or timber; those of cast iron taking an intermediate place. + +Summarising the above considerations, and dealing with the relative +merits of bridges in the different materials, it may be broadly stated +that for conditions at all suitable nothing seems to be superior to +masonry--including in this description first-class brickwork--whether +for road or railway bridges. One pronounced advantage of such bridges +with respect to length of life, is that they are but little affected by +increase of loads. The mass of a masonry arched structure is so great, +and the margin of strength commonly so liberal, that considerable +increments of load may have but little effect upon the reliability of +the structure. + +Cast iron has, for bridges of simple design, a strong claim to the +second place, though its want of ductility is a demerit. It can, +however, have but a limited use in bridge construction, being applicable +only to small girder spans and skilfully-designed arched structures. + +For bridges of moderate span in which the question of cost does not +control the matter, wrought iron should probably come next, steel being +best reserved for those of a larger size, in which weight of the +structure greatly affects economy. + +Timber may be regarded as a material rarely to be used in this country +for structures to occupy a permanent place, unless for urgent economic +reasons of the moment. + +While expressing this general view of the matter, it is to be admitted +that the propriety of these conclusions is somewhat discounted by the +difficulty there now is in obtaining cast iron of the desired +toughness, or wrought iron with promptitude and sufficient variety of +section at a reasonable price. + +It is apparent, also, that the choice of material may be largely +influenced--even determined--by considerations of headway, construction +depth, or character of foundations; so that no very definite rules can +be usefully laid down, though the adoption of unsuitable materials has +not been so unusual as to make these suggestions altogether +purposeless. + + + + +CHAPTER XVI. + +RECONSTRUCTION AND WIDENING--CONCLUSION. + + +The need for the reconstruction of bridges, arising from various causes +which have been treated in the preceding chapters, original weakness or +faults in design, decay or defects, may also be caused by such +extraneous considerations as the growth of loads, widening of the +openings spanned, or improvement of the headway. + +In any case, a precise survey or measuring up of the structure and its +immediate surroundings is required, in the execution of which the +greatest care is desirable, and with respect to which it may be well to +give a few hints. + +The surveying chain, when used, should be tested, the measure of +accuracy required rendering this imperative in a degree peculiar to work +of this class. Linen tapes should also be compared with a reliable steel +tape, and used only where sufficiently accurate for the particular +purpose. A careful and observant man may do very good work with a linen +tape, making just that allowance in the sag of the tape which corrects +for the inevitable stretch; but there is still some uncertainty involved +in its use, and the author prefers to rely upon a steel tape, +notwithstanding the inconvenience commonly experienced from its +intractable nature and liability to damage. + +Instruments used must also be in the best adjustment; as errors, which +in ordinary field work may not be of great importance, are inadmissible +in bridge work. + +It is not necessary here to enter upon the methods of small survey +work, but it may be desirable to point out that abutment walls should be +plumbed for verticality; girders, which are liable to be leaning, +defined in position by reference to their bearings; and generally that +it should never be taken for granted that there is truth in old work, or +that this may be assumed as to line or level. + +In cases where disputes with any local authority as to headway are +likely to arise, it is prudent to supplement the information as to level +of soffits by rods cut to length in strict agreement with the clear +height, before removing the old superstructure. + +It is apparent that in cases where the superstructure is already +condemned, the detail measurements may be confined to that part of the +structure which is to remain, securing only such information as to the +work superseded which may be required in arranging for the new work. + +In taking particulars of skew bridges, needless as the warning may seem, +it is yet necessary to remark that there may be right or left-hand skews +which will not reverse. The author has known a disregard of this to make +serious trouble in two instances. + +Dealing first with reconstruction of the superstructure of railway +under-bridges, these, if small, may not give much trouble, though the +demand for greater strength will, perhaps, involve some difficulty in +working to the limiting construction depth--i.e., the distance from the +top of rail to soffit of bridge--particularly as many old bridges have a +very niggardly allowance in this respect. It may be, and quite commonly +is, necessary to raise the rails a small amount, or, if headway is not +restricted, to lower the soffit. Clearances between the running gauge +and girder-work may also be difficult to secure, more liberal allowances +being now required than formerly. Complications in the character of the +permanent way, so frequently found upon old bridges, should, of course, +be got rid of, if possible; but the endeavour may introduce further +difficulties. Regard must throughout be had to the methods to be adopted +in removing old work and in erecting the new. Perhaps the simplest case +to deal with is that where girders lie parallel to, and under the rails, +with a timber floor upon which the permanent way is carried, as sections +of the road involving pairs of girders may be readily removed, and +replaced by the new girder-work (see Fig. 93). If the deck be of trough +flooring or old rails, the matter may not be so simple, as regard must +then be had to the position of joints in the existing floor, and the new +work be schemed with respect to the number and office of girders which +may be got in at any one breaking of the road. A slight slewing of rails +may sometimes be resorted to on occasion, where this has the effect of +releasing some part of the work not otherwise to be dealt with. + +[Illustration: FIGS. 93 and 94.] + +Bridges having main girders, with timber or trough flooring resting upon +the bottom flanges, or suspended by bolts, will, if carrying many roads, +cause some little difficulty, as the dismantling of any one span +involves the disturbance of others; where, however, many lines are +concerned, it may be feasible to put one or more temporarily out of use, +preserving the continuity of traffic over those which remain, but +refraining from any diversion of the more important roads. + +Somewhat similar troubles occur where main girders with cross-girders at +the lower flanges are found, particularly if the cross-girders are +arranged in line, the ends abutting on each side of the same main girder +webs. It is seldom, however, that this construction is used in bridges +of small span carrying many roads; but where it does occur, it may +necessitate the use of timbering below, to carry the ends of +cross-girders when freed from their supporting main girders. (See Fig. +94.) + +[Illustration: FIG. 95.] + +If it is proposed to use new main and cross-girders, it is desirable to +arrange these in the manner already recommended, the cross-girders not +in line; this has peculiar advantages in reconstruction work, as the +bolting up and riveting of the cross-girder ends is not hampered by +other cross-girder attachments, leaving each piece of floor complete in +itself. Twin main girders are occasionally used with the same object, +and present the advantage of simplicity in erection and independence of +one span from those adjoining (see Fig. 95); but the method is wasteful +of space, and involves a somewhat greater total weight in the main +girders. + +The foregoing observations apply more generally to small single-span +bridges, the operations on which may be effected without any material +disturbance of traffic arrangements; though this can seldom be wholly +avoided, it should be confined, where practicable, to a few hours on a +Sunday. + +The reconstruction of bridges over 70-feet span may have to be dealt +with under more elaborate arrangements, if carrying two lines only, +possibly with single-line working for a period more or less protracted; +or it may be necessary, having regard to the weight of main girders to +be removed, to carry the whole structure upon temporary staging, +supporting the road independently, cutting up and removing the old work, +and later putting the new work in place, either by detailed erection in +its ultimate position, or by erection at one side and drawing across. +The latter method is, however, commonly reserved for cases in which no +special staging is used under the old structure. + +Bridges of a number of openings are usually dealt with by securing full +possession of one road at a time, which for double-line bridges +necessitates single-line working. It is commonly out of the question, +even with moderate spans, to deal with some of these only at a time, and +so avoid continuous possession of one road, for a lengthened period; and +it can only, as a rule, be managed where the ends of the new main +girders do not in any way interfere with those of the old, and where it +is not necessary to reset bed-stones, or make other alterations in the +bearings which necessitate the complete clearance of the pier-tops. In +exceptional cases it may be found possible to arrange for the complete +removal of a small number of moderate spans on a Sunday, and the putting +in place of the new work, as in the case of small single spans. + +Spans erected to one side of the final position, to be later travelled +across, are commonly mounted upon gantry staging, and up to 50 tons +weight may rest directly upon rails well greased. The power adopted to +move the span is usually that of screw or hydraulic jacks, or +occasionally engine haulage, special tackle being in that case necessary +to apply the engine power in the right direction. If the time is +limited, or weight considerable, a more elaborate arrangement by which +the load is supported upon wheels, may be necessary, with a view to +reducing the resistance to a manageable amount. All work which it is +possible to do before shifting into place, including the permanent way, +where this is of a special character, should be executed in advance, +leaving only the rail connections to be made good when the span is in +position. + +Where timber staging is used to carry the permanent way before +dismantling an old structure, it is convenient to begin by placing stout +balks of timber under the sleepers from end to end of the bridge, or +directly under the rails if space is limited; the staging is then +arranged to give support to the running timbers. + +Metallic under-bridges of ample headway, perhaps over coal-workings +(since settled down), or for some less sufficient reason made of metal, +may be cheaply replaced by brick arches built below the old +superstructure, the springings of the arch being checked into the face +of the existing abutments. With stout walls, careful work and good +material will make this an efficient and durable job. + +It being a primary condition of reconstruction work to interfere but +little with ordinary traffic arrangements, single-line working is +avoided wherever practicable; as this, always objectionable, may +necessitate the erection of special signals and signal apparatus, +besides the temporary remodelling of the roads, and in this country may +involve also a Board of Trade inspection--altogether a troublesome and +expensive business. + +Any bridgework which is accompanied by breaking or blocking the road can +only be undertaken by arrangement with the traffic department, after +notice duly given and published in the periodical record of such +matters; it is generally fixed for a Sunday. Preparatory to this, it is +necessary to make all ready by getting as much done beforehand as is +possible. Wherever practicable and prudent, the whole work is released +from its surroundings, masonry cut away, rivets cut out and replaced by +good bolts, nuts removed from holding down bolts, or the bolts cut +through, etc. Particular care should be exercised to ascertain what +remains to be done immediately prior to removal. It is necessary further +to arrange for trucks to be in readiness to receive old material, and +others containing new girder work to be conveniently stationed, having +been loaded up to come right end foremost; engine power, cranes, empty +and loaded trucks, being all marshalled and so placed as to be available +in proper order, and as wanted. There must be no mistake as to what +roads will be fouled by swinging the crane with its load, or as to the +reach of the crane in effecting its work. + +The whole operation to be conducted on any Sunday should be well within +the resources of the men and plant engaged in it, or so managed that it +is a matter of no serious importance if the whole cannot be completed as +originally desired. + +Possession of the roads to be blocked having been secured between +certain hours, if some part only of the work to be carried out has been +completed as the time grows short, any attempt to execute the remainder +may result in checking trains until such time as the line may be +reported clear--a contingency to be avoided--though the temptation to +save another Sunday’s work by delay of a few minutes to some one train +may be considerable. + +In scheming any reconstruction, it may be insisted that at least one +feasible method of carrying out the work must be secured, though it is +the author’s experience that frequently some other method than that +contemplated is in the end adopted, when, some months later, the final +arrangements for fixing are made. The tendency of a zealous erector is +commonly to take full advantage of any facilities offered, with a view +to a moderate amount of work being done at any one time, and to achieve +as much more as he can himself secure by scheming, or a liberal use of +labour; all Sunday work, with attendance of engines and cranes, being of +necessity expensive. + +Railway over-bridges do not commonly present any particular +difficulties. The spans to be dealt with are usually small, and the +weights to be lifted moderate. The height above rails may, however, be +above the lift of any crane; and, for the purpose of raising main +girders, a derrick may become necessary, the rearing and guying of which +may block many roads during the time it is in use. The girders of larger +spans, too unmanageable to be lifted whole, may be erected upon staging; +to secure the requisite headway it may be necessary to build the girders +at a level above that at which they will finally be, lowering them into +position when self-supporting, and after the removal of the staging. + +The widening of railway under-bridges is, as a rule, a matter of no +special difficulty, but some remarks may be of use. Widenings should be +planned with a regard to later reconstruction of the original bridge, if +that is at all likely to be necessary, and with the object that, when +complete, the whole should be a consistent piece of work. + +It may, indeed, happen that widening of a bridge may involve the +remodelling or reconstruction of the old work, to enable the new roads +to be laid down as desired; this is more likely to be necessary where +there exist main girders not competent to take any additional load, and +to duplicate which would sacrifice space between the new and old roads; +or it may be unavoidable because of slewing of the old rails, as part of +a general rearrangement. + +[Illustration: FIG. 96.] + +Dealing with widenings simply, there is often some little trouble in +contriving a connection between the new and the old work, as this may +have to be made under, or close to, the sleeper ends of the existing +roads. It is desirable to arrange this part so that no drilling of old +work for rivets or bolts shall be necessary, there being, in fact, no +strict connection. By judicious scheming, this may be effected, whilst +securing freedom from leakage of water at the joint. (See Figs. 96 and +97.) If tying of the new and old structure is desired, this can usually +be done quite simply, well below the floor at some more accessible +level. + +[Illustration: FIGS. 97 and 98.] + +The strict jointing-up of trough flooring, new to old, at right angles +to the troughs, cannot be contemplated, but may be dealt with by +treating each part independently, the ends being near together, +separated by the space of an inch or so. Each trough end being closed up +by a diaphragm or oak block to prevent ballast dropping through, the top +of the space may be covered by a loose strip, secured to prevent it +shifting, the bottom provided with a gutter of liberal dimensions to +take away leakage, as it is practically impossible to make this +arrangement “drop dry” under the conditions common in executing work of +this kind (see Fig. 98). + +[Illustration: FIGS. 99 and 100.] + +Where trough flooring, new and old, has to be made good parallel to the +troughs, the difficulty of making a direct connection is less marked, +and it is not unusual to introduce a strip cover simply; but if +accessible, the work is still troublesome, as there is commonly a want +of strict alignment and truth as to level, between the new and the old +troughs. It is preferable to arrange for junctions of a more convenient +type, as in Figs. 99 and 100. + +When widening masonry arch bridges by girder-work, it is desirable to +insure that any girders parallel to the masonry face shall be +sufficiently far removed from it to enable painting to be executed. The +space remaining between the girder and the arch may then be bridged by +floor-plates, or an extension of the timber floor if that is adopted. + +In effecting a junction such as this, the author has used the +arrangement shown in Fig. 101, the advantage being that the piece of +connecting-floor is sufficiently wide, and also sufficiently flexible, +to allow the girder-work freedom to deflect without doing harm. The load +carried by the width of floor is, as to one part, delivered well on to +the old masonry, in preference to being imposed near to the face. If it +should for any reason be imperative to place the girder close to the +arch face, it is preferable to scheme the floor so that there shall be +no actual contact, the new floor in that case slightly overhanging the +masonry, as in Fig. 102, or dealt with as in Fig. 103, if depth is +restricted. + +The widening of masonry arch bridges by masonry, calls for no other +remark than that the new work should be free from the old; though it may +be advisable, when the widening is narrow, to tie the new work to the +old in such a way as to permit independent settlement. + +If the widening is exceptionally narrow, there may be no choice but to +bond the new and old work together, and in the best manner, with the +object of minimising the risk of separation. + +[Illustration: FIGS. 101 and 102.] + +[Illustration: FIG. 103.] + +The above matters relative to widenings, though apparently trifling, may +by neglect cause much trouble and expense in maintenance. They +principally concern small bridges, the extension of larger structures +coming rather in the category of independent works. + + +CONCLUSION. + +In bringing these chapters, dealing largely with questions affecting +maintenance, to a close, it may be well to draw attention to the fact +that economy in design (apart from improper reduction of sections) goes +hand-in-hand with economy of upkeep. Given good material, that which +favours low first cost, simplicity of detail, fewness of parts, absence +of smithing, the use of rolled sections, and good depth to girders, +favours also small expenditure in maintenance. The less complex the +design, the easier will it be to keep the structure in order; the less +the number of parts, the fewer will be the connections. Freedom from +smithing eliminates liability to failure at cranks, or other work which +has been subject to fire. It is apparent also that the free use of +rolled instead of built-up sections, reduces the liability to trouble +from bad riveting, or from good riveting overstressed. A liberal depth +to all girders, by reducing deflections, limits the inclination of the +ends and gives the connections a better chance of remaining intact. +Lastly, with work of this character, the labour of scraping and painting +is simplified and cheapened. + +The author wishes to reiterate the statement made in the opening +paragraphs of this book, that all instances of decrepitude, failure, or +peculiar behaviour cited, have been under his direct observation. The +fact is insisted upon simply that the reader may appreciate that the +information is at first hand. + +It has not been thought necessary, nor was it considered desirable, to +indicate the locality of each case referred to; but it may be said that +the matter of these chapters has been accumulating during many years, +and relates to structures under the control of many different bodies. + +The study of old bridges is strongly recommended, particularly with +respect to stress and strain, which in structures new or old, occur +possibly as may be expected--certainly as they must. Consideration of +existing work may thus be a useful check upon the fanciful requirements +of some methods of design. There is a recent tendency, for instance, in +English practice to over-stiffen the webs of plate-girders, such that if +the theory upon which the results are based were true, many old bridges +carrying their loads with no sign of distress, should have failed long +ago. Excess in riveting is a common extravagance, to which the same +criticism may in a less degree apply. Considerable impact allowances for +girders of large span may also be referred to as an application of +empiric theory not justified by experience, which, as in all cases where +such considerations fight with facts, should be modified or rejected. + + + + +INDEX + + + Abutments, leaning, 82, 173 + -- movements of, 158 + -- settlement of, 78 + Adjustment of centre girders, 128 + -- of distributing girders, 120 + Angular distortions, 88 + Arches, equilibrium of, 162 + -- repair of, 163 + Arrangement of cross girders, 21, 175 + Asphalt, 26 + + Ballast, 29 + Bearing pressure on rivets, 47, 51, 57 + Bearings, skew, 4 + Bottom booms, end bays, 18 + Bracing, additional, 117 + -- effects of, 34 + -- flat bars, 37 + -- incomplete, 41 + -- sea piers, 42 + Bridge floors, 20 + -- repairs, 107 + -- surveys, 107 + Bridges, life of, 165 + Breaks in [T] bars, 16 + Buckling of webs, 16 + + Camber, 24, 80 + Cast-iron arches, 80, 145 + -- -- bridges, 141 + -- -- columns, 7,144 + -- -- girders, 141 + -- -- in sea water, 101 + Centre girders, 122 + Cinder ballast, 29 + Cold-blast iron, 141 + Cooling stresses in cast iron, 145 + Construction depth, 173 + Corrugated sheeting, 29 + Cost of centre girders, 135 + -- of maintenance, 168 + Counterbracing, 19 + Cracked bedstones, 3 + -- columns, 7 + -- web plates, 13, 14, 15, 50 + Cross girder arrangement, 21 + -- girders, fixed ends, 22, 118 + -- -- rusted, 29, 97 + -- -- weak, 30, 66 + + Decay and painting, 96 + -- of floor plates, 109 + -- of timber, 28, 150 + Deflection, 85 + -- due to booms and web, 86 + -- exceptional cases, 88 + -- in new and old work, 85 + -- working formulæ, 87 + Deformations, 73 + Depth of girders, 23, 89, 184 + Diagonal ties, 19, 42 + Distortion due to temperature changes, 79, 84 + Distributing girders, 120 + Drainage holes, 25 + “Drop” loads, 89 + Dwarf walls under floors, 26 + + Early steel girders, 68 + Economy, 184 + Effect of earth slips, 157 + -- of floor on deflection, 88 + -- -- -- on stresses, 23, 30 + -- of high stress, 86 + -- of permanent way on stresses, 18 + --of skew on bridge floors, 25 + -- -- -- on centre girders, 131 + -- of transverse bracings, 34 + -- of vibration on masonry, 162 + -- of wave action on sea piers, 42 + End bays, bottom booms, 18 + Equilibrium of masonry arches, 162 + Examination of bridges, 107 + Examples of cast-iron bridges overstressed, 141 + -- of high stress, 70 + -- of life of bridges, 167 + -- of rivet stress, 56 + -- of strengthening, 114 + -- -- -- by centre girders, 131, 134 + Excessive bearing pressure, 51 + + Faulty workmanship, 80 + Fixed ends to cross girders, 22, 118 + Flange stresses, 63, 66, 67 + Flanges, side loaded, 9, 73 + Flat bar bracing, 37 + Flexing of girders, 9, 74, 76 + Flexure curves, 138 + Fractured bedstones, 3 + -- rails, 30 + -- webs, 13, 14, 15, 50 + Fractures in cast iron, 7, 145 + + Girder bearings, 2 + Girders on columns, 7 + -- on masonry, 8 + Girderwork in masonry, 101 + + Headway, 173 + High stress, 61 + -- in cast iron, 141 + -- in rivets, 47, 52 + Holes for drainage, 25 + + Impact, 20, 62 + Inclination of girder ends, 23, 53 + Incomplete bracing, 41 + Initial set, 88 + Interference with traffic, 177 + + Jack arches, 29, 101 + Joints in rails, 29, 109 + -- in trough floors, 28, 180 + Junction between metallic and masonry bridges, 183 + -- -- new and old masonry bridges, 182 + -- -- new and old metallic bridges, 180 + + Lattice girder stresses, 47-66 + Liberal depth to girders, 23, 89, 184 + Life of bridges, 165 + Limit of elasticity, 61 + Linen tapes, 172 + Longitudinal floor girders, 23 + Loose rivets, 21, 25, 51, 53, 56, 109 + + Main girders, 9-17 + Masonry bridges, 157 + -- enduring character of, 161 + Memel timber, 150 + Methods of calculation, 46, 61 + -- of observing deflection, 90 + -- of setting out deflection curves, 138 + Movements of abutments, 158 + -- of cast-iron bridge, 82 + -- of piers, 42, 83, 159 + -- of rollers, 7 + -- of wrought-iron bridges, 4, 21, 38, 73 + + New members to old work, 116 + + Oiling steelwork, 99 + Old drawings unreliable, 108 + -- rivets, 21, 51, 54, 55 + Open webs, 17 + Overhead bracing, 39 + -- girders, 118 + + Painting, 98 + Parapets, 79 + Permissible stress in old work, 110 + Piers, movements of, 42, 83, 159 + -- out of plumb, 159 + Piles, decay of, 102, 150 + Pitch pine, 28 + Plasticity, 61 + Plate webs, 9 + Plated floors, 23, 25, 30 + Pointing masonry, 164 + Proposed rivet stresses, 58 + + Quickly applied loads, 89 + + Rail joints, 29, 109 + Rails, breaks in, 30 + Reaction of cross girder with centre support, 127 + Red-lead, 98, 100 + Relative merits of bridges, 169 + Relief by centre girders, 122 + Repainting, 100 + Repair of bridges, 107, 147, 155, 163 + -- of timber piles, 156 + Replacing flange plates, 110 + -- rivets, 111 + Resistance of cast iron to rust, 101 + Riveted connections, 45, 86 + Rivets in cramped positions, 20 + -- in cross girder ends, 21, 49, 53, 54 + -- in road bridges, 60 + -- in webs of main girders, 46 + -- spacing of, 60, 80 + -- stresses in, 56 + Rocking of piers, 8, 83, 159 + Roller bearings, 7 + Rubble masonry, 161-164 + Running load and deflection, 95 + Rusting, instances of, 29, 96 + -- of steelwork, 99 + -- over sea-water, 98 + + Sag in timber bridges, 150 + -- of tapes, 172 + Scour under piers, 161 + Sea piers, 42, 102 + Setting bedstones, 3, 129, 176 + Settlements, 76, 157 + Skew bearings, 4 + -- bridges, right and left, 173 + -- -- floors, 25 + Skirting plate, 26 + Slope of girder ends, 92 + Softening of cast-iron in sea-water, 101 + Spacing of rivets, 60, 79 + Spread of abutments, 157 + Spring joints, 23 + Steel trough girders, 68 + -- troughing, 70 + Stiffening girders from floor, 12, 40 + -- to webs, 16, 38, 185 + Stop piers, 158 + Strength of light top booms, 40 + Strengthening of bridges, 107, 122 + -- bridge floors, 118 + -- cross girders, 123 + Stress in plated floors, 31 + Study of old bridges, 185 + + Tall piers, 42, 159 + Timber bridges, 149 + -- floors, 27 + -- staging, 177 + Top booms, 18 + Traffic during reconstruction, 177 + Transverse bracing, 34, 117 + Trough floors, 27, 180 + -- girders, 50, 74 + [T] stiffeners, breaks in, 16 + Twin girders, 15, 75 + Twisting of girders, 11, 68, 73 + -- -- -- corrected, 12 + Types of reconstruction, 174 + + [U]-shaped booms, 18 + Uncomplicated stress, 62 + Uniform pressure on bearings, 6 + + Value of E in deflection formulæ, 87 + Vibration, 162 + + Wasted webs, 14, 29, 96 + Water, scour of, 161 + Web buckling, 16 + -- plates, cracked, 13, 14, 15, 50 + -- rivets, 46, 50 + -- stiffening, 16, 38, 185 + Widening masonry bridges, 182 + -- metallic bridges, 179 + Wide spaced rivets, 79 + Wind pressure, 41, 43 + + Yielding of piers, 8, 83, 159 + + + LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, + GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E. + + + + +Transcriber's Notes: + +The text of the original work (including inconsistent spelling, +hyphenation, formatting etc.) has been retained, except as mentioned +below. + +The slight differences between the Table of Contents and the text have +not been changed. + +Changes made to the text: + +Some punctuation errors and obvious typographical errors have been +corrected silently. + +Several illustrations have been moved to where they are described in the +text. + +Page 123, formula (2): the original shows an unclear superscript after +the first L. As described in the following line of the text, this has +been changed to L{_l_}. + + + + + +End of Project Gutenberg's The Anatomy of Bridgework, by William Henry Thorpe + +*** END OF THE PROJECT GUTENBERG EBOOK 44371 *** |